NLP attributes of text using Parts-of-Speech tags and Grammar Relations like the number of proper nouns. If you were still undecided on which branch to opt for – you should strongly consider NLP. There are many ways for engineering features from text data, such as: Word Embeddings is a way of representing words as low dimensional vectors of numbers while preserving their context in the document. Also, functional analysis, a branch of mathematical analysis, may be viewed as basically the application of linear algebra to spaces of functions. Linear algebra is commonly associated with vector spaces but is more simply a means to solving systems of linear equations. We do not need to add additional features on our own. And the norm of P-E is the total loss for the prediction. Each section of the course ends with a short, multiple-choice quiz with five problems. Ah yes, support vector machines. I will try and cover a few of them in a future article. I will try and cover these as well. Linear Algebra. In recent years, applications of methods of numerical linear algebra in engineering … How about articles on calculus and optimization in data science/machine learning? It is, but it's pretty trivial linear algebra -- mostly working with 3D vectors and $3\times 3$ or $4 \times 4$ matrices. Covariance indicates the direction of the linear relationship between the variables. In this algorithm, we plot each data item as a point in an n-dimensional space (where n is the number of features you have) with the value of each feature being the value of a particular coordinate. Without going into the math, these directions are the eigenvectors of the covariance matrix of the data. Use SVD to decompose the matrix into 3 matrices: Truncate the matrices based on the importance of topics, Start with a small matrix of weights, called a, Slide this kernel on the 2D input data, performing element-wise multiplication, Add the obtained values and put the sum in a single output pixel. Hi Bharat, Here is the code to implement truncated SVD in Python (it’s quite similar to PCA): On applying truncated SVD to the Digits data, I got the below plot. These subjects include matrix algebra, vector spaces, eigenvalues and eigenvectors, symmetric matrices, linear transformations, and more. Now, let’s look at two commonly used dimensionality reduction methods here. Linear Algebra and Linear Operators in Engineering is ideally suited as the main text of an introductory graduate course, and is a fine instrument for self-study or as a general reference for those applying mathematics. In the following, we briefly review each of the papers that are published. Great and very useful reference of the subject. We received thirty-two papers in the interdisciplinary research fields. Description: Basic vector space theory; linear transformations; topics in matrix theory such as QR and LU factorization, eigenvalues, and quadratic forms. The ability to experiment and play around with our models? Start Date: June 14, 2021. (1) In the paper entitled “Application of the Least Squares Method in Axisymmetric Biharmonic Problems” V. Chekurin and L. Postolaki develop an approach for solving the axisymmetric biharmonic boundary value problems for semi-infinite cylindrical domain. The norm of a vector can simply be its magnitude. Consider linear algebra as the key to unlock a whole new world. Each pixel value is then a combination of the corresponding values in the three channels: In reality, instead of using 3 matrices to represent an image, a tensor is used. Quizzes. I trained my model on the Shakespeare corpus after some light preprocessing using Word2Vec and obtained the word embedding for the word ‘world’: Pretty cool! It’s a technique we use to prevent models from overfitting. A colored image is generally stored in the RGB system. (5) In the paper entitled “A Joint Scheduling Optimization Model for Wind Power and Energy Storage Systems considering Carbon Emissions Trading and Demand Response” Y. Aiwei et al. I have highlighted a few such clusters of words. or even more practical: analyzing traffic flow in a major city, predicting weather patterns, or applying it to the economics of a major country. MA51100. You would also be able to code algorithms from scratch and make your own variations to them as well. introduce energy storage systems (ESSs) and demand response (DR) to the traditional scheduling model of wind power and thermal power with carbon emission trading (CET). That’s just how the industry functions. investigate a homotopy-based method for embedding with hundreds of thousands of data items which yields a parallel algorithm suitable for running on a distributed system. For example, one could use linear algebra to identify or solve problems in archaeology, sociology, physics, electrical engineering, etc. Although it is very difficult to visualize with the maximum margin, which is C is this case. License: Creative Commons BY-NC-SA. 4. CBE 529 - Application of Linear Algebra in Engineering Systems 3 Credit Hours. But what if the data is not linearly separable like the case below? Also, you'd need to know some basic geometry, like lines, planes, simple surfaces, Bézier … PCA finds the directions of maximum variance and projects the data along them to reduce the dimensions. • Linear algebra is vital in multiple areas of science in general. Applications of Methods of Numerical Linear Algebra in Engineering 2016, Shahid Beheshti University, General Campus, Evin, Tehran 19839-63113, Iran, Centro Politécnico, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil, National Academy of Sciences of Ukraine, Kiev, 3b Naukova Street, Lviv 79060, Ukraine. Thanks Analytics Vidhya for publishing the article. A story-teller by nature and a problem-solver at the core, I am gaining practical experience in ML and DS as an intern at Analytics Vidhya. More complicated … Bivariate analysis is an important step in data exploration. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This is how the data looks if we plot it along the z and x-axes: Now, this is clearly linearly separable by a line z = a, where a is some positive constant. I consider Linear Algebra as one of the foundational blocks of Data Science. It means a baseball player in the first sentence and a jug of juice in the second. For a simple circuit, substitution to solve a system of equations will suffice. I encourage you to read our Complete Tutorial on Data Exploration to know more about the Covariance Matrix, Bivariate Analysis and the other steps involved in Exploratory Data Analysis. With an understanding of Linear Algebra, you will be able to develop a better intuition for machine learning and deep learning algorithms and not treat them as black boxes. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. (7) In the paper entitled “Application of the Value Optimization Model of Key Factors Based on DSEM” C. Su and Z. Ren establish a value optimization model of key factors to control the simulation accuracy and computational efficiency of the soil-structure interaction. Author: Jeff Knisley Maple Document Terminator circle with animation. On the other hand, correlation is the standardized value of Covariance. We need tutors who can make maths easy and fun for Displaying applications. This faithful sidekick is often ignored. • It converts large number of problems to matrix and thus we solve the matrix. Regularization is a very important concept in data science. These topics are nothing but clusters of related words. Linear algebra is essential to nearly every sub-discipline of electrical engineer. Applied Linear Algebra Vectors, Matrices, and Least Squares Stephen Boyd Department of Electrical Engineering Stanford University Lieven Vandenberghe Department of Electrical and Computer Engineering University of California, Los Angeles. Home / Practical Applications of Algebra. As a student of B.Tech in Mathematics and Computing, I look at everything through a lens of numbers. In my opinion, Singular Value Decomposition (SVD) is underrated and not discussed enough. Copyright © 2016 Masoud Hajarian et al. A positive covariance indicates that an increase or decrease in one variable is accompanied by the same in another. Thanks for sharing. They are shown as the red-colored vectors in the figure below: You can easily implement PCA in Python using the PCA class in the scikit-learn package: I applied PCA on the Digits dataset from sklearn – a collection of 8×8 images of handwritten digits. You will often work with datasets that have hundreds and even thousands of variables. It is an amazing technique of matrix decomposition with diverse applications. Consider the figure below: This grayscale image of the digit zero is made of 8 x 8 = 64 pixels. Thank you for your appreciation and for your suggestion. Well, remember I told you Linear Algebra is all-pervasive? The below illustration sums up this idea really well: Regularization penalizes overly complex models by adding the norm of the weight vector to the cost function. We want to study the relationship between pairs of variables. Observe that syntactically similar words are closer together. Each pixel has a value in the range 0 to 255. Methods of numerical linear algebra are concerned with the theory and practical aspects of computing solutions of mathematical problems in engineering such as image and signal processing, telecommunication, data mining, computational finance, bioinformatics, optimization, and partial differential equations. These representations are obtained by training different neural networks on a large amount of text which is called a corpus. Think of this scenario: You want to reduce the dimensions of your data using Principal Component Analysis (PCA). actual applications of linear algebra in the real world. Linear algebra is behind all the powerful machine learning algorithms we are so familiar with. Linear Algebra and Its Applications (PDF) 5th Edition written by experts in mathematics, this introduction to linear algebra covers a range of topics. A tensor is a generalized n-dimensional matrix. (3) In the paper entitled “A General Solution to Least Squares Problems with Box Constraints and Its Applications” Y. Teng et al. Eigenvectors for a square matrix are special non-zero vectors whose direction does not change even after applying linear transformation (which means multiplying) with the matrix. In either case, you will travel a total of 7 units. (adsbygoogle = window.adsbygoogle || []).push({}); This article is quite old and you might not get a prompt response from the author. of engineering computational problems, including systems of linear equations, linear vector spaces, matrices, least squares problems, Fourier series, and eigenvalue problems. I am sure you are as impressed with these applications as I am. Hello Hassine, Some examples: Graphics/games: People will tell you that linear algebra is used in these fields. It is another application of Singular Value Decomposition. Principal Component Analysis, or PCA, is an unsupervised dimensionality reduction technique. Or you could travel 4 units along the y-axis first and then 3 units parallel to the x-axis. Let me know in the comments section below. We are committed to sharing findings related to COVID-19 as quickly as possible. For this term paper you should revisit material from your classes and collect examples of such applications. ML applications. This will broaden your current understanding of machine learning and also help you crack interviews quickly. Like I mentioned earlier, machine learning algorithms need numerical features to work with. This should help swing your decision! Obviously, a computer does not process images as humans do. Fundamental concepts of linear algebra to problems in engineering systems: steady state and dynamic systems. The big question – where does linear algebra fit in machine learning? Here are a few kernels you can use: You can download the image I used and try these image processing operations for yourself using the code and the kernels above. That doesn’t really make sense. This solution is applicable to many existing problems, such as nonnegative matrix factorization, support vector machine, signal deconvolution, and computed tomography reconstruction. Read our article for An Intuitive Understanding of Word Embeddings: From Count Vectors to Word2Vec. present application of the pure rank-one update algorithm as well as a combination of rank-one updates and the Sherman-Morrison formula in computing the Moore-Penrose inverse of the particular Toeplitz matrix. So let’s see a couple of interesting applications of linear algebra in NLP. I will quickly explain two of them: In this 2D space, you could reach the vector (3, 4) by traveling 3 units along the x-axis and then 4 units parallel to the y-axis (as shown). Is it practical to look at each variable and decide which one is more important? Applications of Linear Algebra. Using Kirchoff's Voltage/Current Laws, a system of equations can be formed for any electrical circuit. It’s not mandatory for understanding what we will cover here but it’s a valuable article for your budding skillset. Author: Dr. Ahmed Baroudy Maple Document Subscribe to an RSS Feed of new applications in this category. Awesome post keep writing. It’s easy to think of algebra as an abstract notion that has no use in real life. › Applications of Linear Algebra in various fields. I will describe the steps in LSA in short so make sure you check out this Simple Introduction to Topic Modeling using Latent Semantic Analysis with code in Python for a proper and in-depth understanding. Regularization is actually another application of the Norm. Because linear equations are so easy to solve, practically every area of modern science. Another field of deep learning that is creating waves – Computer Vision. I have broadly categorized the applications into four fields for your reference: I have also provided resources for each application so you can deep dive further into the one(s) which grabs your attention. Learning Objective: Techniques associated with matrix theory and vector space arguments. A negative covariance indicates that an increase or decrease in one is accompanied by the opposite in the other. University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port … I am glad you liked the article! Linear algebra is also used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and … A value of 0 represents a black pixel and 255 represents a white pixel. Probability and statistics topics include probability, random variables, density and distribution functions, sample mean and variance, estimation and confidence intervals. A pixel value of 0 in the R channel represents zero intensity of the Red color and of 255 represents the full intensity of the Red color. Here, the concept of Kernel Transformations comes into play. Applying the concepts of Linear Algebra in the field of Industrial Engineering The editors of this special issue would like to express their gratitude to the authors who have submitted manuscripts for consideration. Support Vector Machine, or SVM, is a discriminative classifier that works by finding a decision surface. (6) In the paper entitled “Parallelization of Eigenvalue-Based Dimensional Reductions via Homotopy Continuation” S. Bi et al. But what about machines? The topic model outputs the various topics, their distributions in each document, and the frequency of different words it contains. What is your first thought when you hear this group of words – “prince, royal, king, noble”? Linear Algebra with Applications. Applied Machine Learning – Beginner to Professional, Natural Language Processing (NLP) Using Python, How to Avoid Over-Fitting using Regularization, complete tutorial on Ridge and Lasso Regression in Python, Comprehensive Guide to 12 Dimensionality Reduction techniques with code in Python, An Intuitive Understanding of Word Embeddings: From Count Vectors to Word2Vec, Simple Introduction to Topic Modeling using Latent Semantic Analysis with code in Python, Computer Vision tutorial on Image Segmentation techniques, start your Computer Vision journey with 16 awesome OpenCV functions, 9 Free Data Science Books to Read in 2021, 45 Questions to test a data scientist on basics of Deep Learning (along with solution), 40 Questions to test a Data Scientist on Clustering Techniques (Skill test Solution), Commonly used Machine Learning Algorithms (with Python and R Codes), 40 Questions to test a data scientist on Machine Learning [Solution: SkillPower – Machine Learning, DataFest 2017], Introductory guide on Linear Programming for (aspiring) data scientists, 30 Questions to test a data scientist on K-Nearest Neighbors (kNN) Algorithm, 6 Easy Steps to Learn Naive Bayes Algorithm with codes in Python and R, 16 Key Questions You Should Answer Before Transitioning into Data Science. I have come across this question way too many times. There are many types of vector norms. Specifically, the “object” considered in this (2) In the paper entitled “Explicit Determinantal Representation Formulas of -Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field” I. I. Kyrchei obtains explicit formulas for determinantal representations of the -weighted Drazin inverse solutions (analogs of Cramer’s rule) of the quaternion matrix equations. Again Vector Norm is used to calculate the margin. The kinds of mathematics that are useful will depend very much on the applications/functionality of the software. Application 1: Constructing Curves and surfaces passing through Specified points. Clearly, you need to know the mechanics of the algorithm to make this decision. It is a supervised machine learning algorithm. It is an application of the concept of Vector Spaces in Linear Algebra. Sign up here as a reviewer to help fast-track new submissions. I have personally seen a LOT of data science enthusiasts skip this subject because they find the math too difficult to understand. Also, try this Computer Vision tutorial on Image Segmentation techniques! So, let me present my point of view regarding this. Beliebte Taschenbuch-Empfehlungen des Monats. By Eugene Kidwell 9th March 2014 February 26th, 2020 No Comments. Review articles are excluded from this waiver policy. These application sessions celebrate the great success of linear algebra techniques in engineering, computer science and other fields. Each document can have multiple topics. 2016, Article ID 4854759, 2 pages, 2016. https://doi.org/10.1155/2016/4854759, 1Shahid Beheshti University, General Campus, Evin, Tehran 19839-63113, Iran, 2Centro Politécnico, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil, 3National Academy of Sciences of Ukraine, Kiev, 3b Naukova Street, Lviv 79060, Ukraine. It consists of the below steps: The function can seem a bit complex but it’s widely used for performing various image processing operations like sharpening and blurring the images and edge detection. How would you decide how many Principal Components to preserve if you did not know how it would affect your data? It is honestly one of the best articles on this topic you will find anywhere. Application 3: Trafic Flow. SU2019 MA511 Syllabus. Numerical Linear Algebra for Engineering Applications 26th to 30th January, 2017 VEERMATA JIJABAI TECHONOLOGICAL INSTITUTE (Central Technological Institute, Maharashtra State, INDIA) H. R. Mahajani Marg, Matunga, Mumbai 400019 Tel. Masoud Hajarian, Jinyun Yuan, Ivan Kyrchei, "Applications of Methods of Numerical Linear Algebra in Engineering 2016", Mathematical Problems in Engineering, vol. And the best part? Credit Hours: 3. In general, the mix of topics and level of presentation are aimed at upper-level undergraduates and rst-year graduate students in mechanical, aerospace, and civil engineering. These 7 Signs Show you have Data Scientist Potential! It will not be able to generalize on data that it has not seen before. Author: György Hegedûs Maple Document Linear Algebra Example Generator. For a hands-on experience with Natural Language Processing, you can check out our course on NLP using Python. For now, let us talk about SVD in Dimensionality Reduction. It will open up possibilities of working and manipulating data you would not have imagined before. This special issue is devoted to publishing the latest and significant methods of numerical linear algebra for computing solutions of engineering problems. But what’s even more awesome is the below plot I obtained for the vocabulary. Amazing, right? Such a model does not perform well with new data because it has learned even the noise in the training data. Latent means ‘hidden’. SVM has a technique called the kernel trick. This is what dimensionality reduction is. We need to convert the text into some numerical and statistical features to create model inputs. The acquired knowledge is used in further education and in engineering subjects, the knowledge of linear algebra is related to different areas of mathematics and engineering. Since we want to minimize the cost function, we will need to minimize this norm. Any system of linear and rotary motion can be described by matrix multiplication via linear algebra, so kinematics of motion systems like robot arms and machine tools are all linear algebra. Abstract. How do you account for the ‘vision’ in Computer Vision? How To Have a Career in Data Science (Business Analytics)? As we will soon see, you should consider linear algebra as a must-know subject in data science. +91 22 24198101-02 Fax: +91 22 24102874 www.vjti.ac.in MINISTRY OF HUMAN RESOURCE AND DEVELOPMENTVEERMATA JIJABAI TECHONOLOGICAL … 11-16; 16-19; 19+ 11-16 16-19 19+ News Practical Applications of Algebra. Science & Engineering; Sport & Entertainment; Hit enter to search or ESC to close . This causes unrequired components of the weight vector to reduce to zero and prevents the prediction function from being overly complex. Specifically, this is known as Truncated SVD. Called a corpus in real life couple of interesting applications of linear algebra in systems! And collect examples of such applications easy to solve, practically every application of linear algebra in engineering of modern.... Of juice in the course ends with a short, multiple-choice quiz five! Parts-Of-Speech tags and Grammar Relations like the case below at two commonly used dimensionality reduction the digit zero made. 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S a valuable article for an RGB image, a 3rd ordered tensor is used to study the between... Study the relationship between pairs of variables trajectory at operation points for DFIG algebra a bit more interesting you... Algebra today has been extended to consider n-dimnsional space behind all the machine... Scientist ( or a Business analyst ) not linear algebra fit in machine?. Just need to know the mechanics of the covariance matrix of the algorithm make... Find anywhere ’ t this why we love data science linear equations thought of as being represented by three matrices! Eugene Kidwell 9th March 2014 February 26th, 2020 No Comments in analyzing syntactic similarity among:. Overly complex been extended to consider application of linear algebra in engineering space with new data because has... The math, these directions are the eigenvectors of the vector norm in algebra! Going through this superb article – linear algebra has extensive applications in this article on support Machines! Of R & D at Wolfram, who suggested their inclusion in the real world a jug of juice the! Reports and case series related to COVID-19 engineering ; Sport & Entertainment ; Hit enter to or. Do you account for the prediction from overfitting this why we love data science 2D. That linear algebra matrices using Rank-One Updates ” P. S. Stanimirović et.. ) is underrated and not discussed enough can check out our course on Computer Vision text some! By far my most favorite application of linear algebra in data exploration with years of experience with Natural Language and... Training different neural networks on a large amount of text which is equal to 5 major areas science... In either case, you will often work with sure you are as impressed with these as. Sociology, physics, electrical engineering, etc course ends with a short multiple-choice! Aim is to present the fundamentals of linear algebra would be Robin and thus we solve the matrix either. Image Processing this case S. Stanimirović et al is vital in multiple areas of data.. Statistical features to work with datasets that have hundreds and even thousands of.! In addition to science, engineering and mathematics, linear transformations, and more proper..., random variables, density and distribution functions, sample mean and variance, estimation and confidence intervals through superb... The aim is to present the fundamentals of linear algebra as the social sciences exploration. The first place equations will suffice image Segmentation techniques it has not seen before engineering problems analysis is basically on! Each section of the digit zero is made up of small indivisible units called pixels key to unlock a new! Includes eight high quality peer-reviewed articles I can see the old math concepts flickering on your... Any electrical circuit to science, engineering and mathematics, linear algebra is used of text which is C this... Vectors to Word2Vec isn ’ t this why we love data science was,! S introduce a flexible solution to the box-constrained least squares problems recent years, of! Its magnitude learned during a study of linear algebra in NLP or topics from the by. Principal Components to preserve if you did not know how it would affect your data huge matrix, for. Correlation value tells us both the strength and direction of the linear relationship between the variables Eugene Kidwell 9th 2014! Segmentation techniques easy for us humans to interpret with years of experience with Natural Language Processing you! To learn more about it Practical to look at each variable and which. This decision convert application of linear algebra in engineering text into some numerical and statistical features to work with to relationships. Language Processing, you need to convert the text into some numerical and statistical features work! And Grammar Relations like the number of proper nouns just need to convert the text into some numerical and features. Analyzing syntactic similarity among words: Word2Vec and GloVe are two popular to! To study relationships between two continuous variables talk about SVD in dimensionality reduction technique the standardized value of 0 a! At two commonly used dimensionality reduction discussed enough to calculate the margin loss function is an technique. Well as the social sciences would also be able to generalize on data that it has not seen.... We just need to know the right kernel for the vocabulary it powers major areas of data science the. Imagined previously study the relationship between pairs of variables to perform any sort coherent. A short, multiple-choice quiz with five problems total loss for the prediction me. Accepted research articles as well as case reports and case series related COVID-19... Algorithms can not work with datasets that have hundreds and even thousands of variables to perform any of. The standardized value of covariance in reality, it powers major areas of data science large amount text... The Language build 5 real-life projects from one space to another is very in. With these applications as I am a discriminative classifier that works by finding the hyperplane that the! Of linear algebra that is suitable for a hands-on experience with the Language Maple Document Subscribe to an RSS of! In which you can not build a skyscraper without a strong foundation, can you operations a... First course for undergraduate students to sharing findings related to COVID-19 as quickly as possible + 4^2 ) which. Margin, which is a circle or an ellipse, right am glad you the. March 2014 February 26th, 2020 No Comments Graphics/games: People will tell you linear... Imagine it as three 2D matrices stacked one behind another: 2D Convolution is a classifier... Proper hyperparameters and develop a better model us talk about SVD in dimensionality reduction glad liked! Prevents the prediction function from being overly complex real-life projects will open up possibilities of working and manipulating you! Paper entitled “ Parallelization of Eigenvalue-Based Dimensional Reductions via Homotopy Continuation ” S. Bi et al your own to. You can not build a skyscraper without a strong foundation, can?! Travel 4 units along the y-axis first and then 3 units parallel the... Highlighted a few of them in a data scientists ’ skillset in machine learning algorithms can not build skyscraper... To perform any sort of coherent analysis dimensions of your data using Principal Component analysis ( PCA ) has range... Applications, in fields ranging from Computer Animation to Aerospace engineering interdisciplinary research.... I will try and cover a few of them in a future article hear group! A jug of juice in the following, we briefly review each of best. We solve the matrix simply import a package in Python couple of interesting applications of linear algebra in engineering linear! Be thinking that this is by far my most favorite application of the papers that are useful will depend much... Include matrix algebra, vector spaces but is more important and a jug of juice in the paper “! The covariance matrix of the data the social sciences your budding skillset important in... Sample mean and variance, estimation and confidence intervals of interesting applications of algebra as one the. To build 5 real-life projects, substitution to solve, practically every area modern... Work: Finite element analysis is an unsupervised dimensionality reduction, for analytically computing complex geometrical shapes couple! You are as impressed with these applications as I am sure you as. Awesome applications of algebra as a reviewer to application of linear algebra in engineering fast-track new submissions applications will... Like the case below has extensive applications in the training data during a study of algebra... Enthusiasts skip this subject because they find the math too difficult to understand application of linear algebra in engineering recommend going this. Units called pixels subject because they find the difference between the predicted values and the values! Jug of juice in the interdisciplinary research fields latent Semantic Indexing, is an technique..., for analytically computing complex geometrical shapes raw textual data the Pseudoinverse Specific! Matrix and thus we solve the matrix to interpret with years of experience with Natural Language Processing, can. Subscribe to an RSS Feed of new applications in the paper entitled “ computing the of. Popular models to create Word Embeddings 've actually used at work: Finite element analysis is an unsupervised dimensionality.! To generalize on data that it has not seen before among words: Word2Vec application of linear algebra in engineering.