# Linear Algebra

## Software

### PC

* [SpeedCrunch](https://speedcrunch.org/)–open source software, fast, simple
* [GNU Octave](https://www.gnu.org/software/octave/index)–open source software
* [Online Octave](https://octave-online.net/) - online GNU Octave
* [Matlab](https://www.mathworks.com/products/matlab.html)–proprietary
* [Anaconda for Python Data Science Programming](https://www.anaconda.com/products/individual)

### Android

* [Madona](https://play.google.com/store/apps/details?id=com.krazeapps.octaveprogrammingcompiler)
* [Anoc Octave Editor](https://play.google.com/store/apps/details?id=verbosus.anoclite)

## MOOC

* [edX - Linear Algebra - Foundations to Frontiers](https://www.edx.org/course/linear-algebra-foundations-to-frontiers) : good interactive HW exercises, very clear instruction and time-efficient
* [MIT OCW - Linear Algebra by Gilbert Strang](https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/) [Youtube](https://www.youtube.com/watch?v=YrHlHbtiSM0): Gilbert Strang is good.
* [Coursera - Mathematics for Machine Learning: Linear Algebra](https://www.coursera.org/learn/linear-algebra-machine-learning)
* [Algebra 1 - Khan Academy](https://www.khanacademy.org/math/algebra) and [Algebra 2 - Khan Academy](https://www.khanacademy.org/math/algebra2)

## Youtube

* [3Blue1Brown Youtube](https://www.youtube.com/watch?v=fNk_zzaMoSs\&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)
* [MathTheBeautiful Youtube](https://www.youtube.com/c/MathTheBeautiful/playlists?view=50\&sort=dd\&shelf_id=2)
* [Grant Sanderson](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)

## List of Books

* [Overview of Linear Algebra Fundamentals](https://github.com/photonlines/Intuitive-Overview-of-Linear-Algebra-Fundamentals)
* [Opentext Uleth](https://opentext.uleth.ca/linalg.html)

## Proprietary Books

* [Handbook of Linear Algebra by Leslie Hogben](https://www.google.com/books/edition/_/5HxcAgAAQBAJ?hl=en)
* [Introduction to Applied Linear Algebra Vectors, Matrices, and Least Squares by Stephen Boyd](https://www.cambridge.org/core/books/introduction-to-applied-linear-algebra/4D69AF22E38303FE20FFEEFDCE0E7F96)
  * [Python Language Companion to Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares](https://ses.library.usyd.edu.au/handle/2123/21370)
* [Linear Algebra and Its Applications by David C. Lay](https://books.google.co.id/books?id=apXfrQEACAAJ\&redir_esc=y)
* [Elementary Linear Algebra: Application Version by Howard Anton](https://books.google.co.id/books?id=loRbAgAAQBAJ\&redir_esc=y)
* [Elementary Linear Algebra by Ron Larson](https://books.google.co.id/books/about/Elementary_Linear_Algebra.html?id=rqWCVMYk5mEC\&redir_esc=y)
* [Linear Algebra Ideas and Applications by Richard C. Penney](https://books.google.com/books/about/Linear_Algebra.html?id=0avYCgAAQBAJ\&redir_esc=y)
* [Linear Algebra Done Right by Sheldon Axler](https://books.google.com/books?id=ovIYVIlithQC)
* [A Concise Text on Advanced Linear Algebra by Yisong Yang](https://books.google.com/books?id=SZJEBQAAQBAJ)

## Free Books

* [An Intuitive Overview of Linear Algebra Fundamentals](https://github.com/photonlines/Intuitive-Overview-of-Linear-Algebra-Fundamentals)
* [Introduction to Linear Algebra by Thomas L. Scofield - PDF](https://sites.calvin.edu/scofield/courses/m231/S14/laNotes.pdf)
* [Algebra by Paul Dawkins](https://tutorial.math.lamar.edu/classes/alg/alg.aspx) [PDF](https://tutorial.math.lamar.edu/GetFile.aspx?file=B,9,N)
* [Linear Algebra Abridged by Sheldon Axler](https://linear.axler.net/LinearAbridged.html)
* [Intuitive Overview of Linear Algebra Fundamentals](https://github.com/photonlines/Intuitive-Overview-of-Linear-Algebra-Fundamentals)
* [Linear Algebra A Course for Physicists and Engineers by Arak M. Mathai](https://www.degruyter.com/view/title/534099) License: CC-BY-NC-ND
* [Linear Algebra](https://www.math.ucdavis.edu/~linear/) License: CC-BY-NC
* [Math 1410 Elementary Linear Algebra by Sean Fitzpatrick](https://github.com/ULeth-Math-CS/Math1410-Text) License: CC-BY-NC
* [Lecture Notes for Math 3410, with Computational Examples by Sean Fitzpatrick](https://www.cs.uleth.ca/~fitzpat/math3410/linalg-notes-with-computations.html) License: CC-BY-NC
* [Linear Algebra with Application by Keith Nicholson](https://lyryx.com/linear-algebra-applications/) [PDF](https://lila1.lyryx.com/textbooks/OPEN_LAWA_1/marketing/Nicholson-OpenLAWA-2019A.pdf) License: CC-BY-NC
* [Immersive Linear Algebra](https://immersivemath.com/ila/index.html)
* [Introduction to Applied Linear Algebra–Vectors, Matrices, and Least Squares](https://vmls-book.stanford.edu/)
  * [PDF](https://vmls-book.stanford.edu/vmls.pdf)
  * [Lecture Slides](https://vmls-book.stanford.edu/vmls-slides.pdf)
  * [Julia Companion](https://vmls-book.stanford.edu/vmls-julia-companion.pdf)
  * [Additional Exercises](https://stanford.edu/class/engr108/103exercises.pdf)
  * [Python Companion](https://ses.library.usyd.edu.au/handle/2123/21370)
  * [Julia and Python language notebooks](https://github.com/vbartle/VMLS-Companions)

## Open Books

* [Linear Algebra, Theory And Applications by Kenneth Kuttler](https://open.umn.edu/opentextbooks/textbooks/linear-algebra-theory-and-applications) [PDF](https://lila1.lyryx.com/textbooks/KUTTLER_1/marketing/Kuttler-LinearAlgebra-AFirstCourse-2017A.pdf) License: CC-BY
* [Linear Algebra by Jim Hefferon](https://hefferon.net/linearalgebra/) License : GFDL and CC-SA
  * [PDF](https://joshua.smcvt.edu/linearalgebra/book.pdf)
  * [Solution Answer](https://joshua.smcvt.edu/linearalgebra/jhanswer.pdf)
  * [Videos](https://www.youtube.com/playlist?list=PLwF3A0R8OzMoMlE1-SaEh8h9VqUlO-r52)
  * [Slides](https://joshua.smcvt.edu/linearalgebra/slides.zip)
  * [Lab Manual](https://joshua.smcvt.edu/linearalgebra/lab.pdf)
  * [Latex Source](https://gitlab.com/jim.hefferon/linear-algebra)
  * [Take Home Exercises](https://joshua.smcvt.edu/linearalgebra/problems2014.zip)
* [Interactive Linear Algebras by Dan Margalit](https://textbooks.math.gatech.edu/ila/index.html) License: GPL/GFDL Pretext Book
* [Discover Linear Algebra by Jeremy Sylvestre](https://sites.ualberta.ca/~jsylvest/books/dla.html) License: GFDL Pretext Book
  * [1-Semester Discover Linear Algebra](https://sites.ualberta.ca/~jsylvest/books/DLA1/frontmatter-1.html)
  * [2-Semesters Discover Linear Algebra](https://sites.ualberta.ca/~jsylvest/books/DLA/frontmatter-1.html)
* [A First Course in Linear Algebra by Robert A. Beezer](https://linear.ups.edu/) [PDF](https://linear.ups.edu/download/fcla-3.50-print.pdf) or its public beta version of [A First Course in Linear Algebra](https://linear.ups.edu/fcla/index.html) License: GFDL
* [Understanding Linear Algebra by David Austin](https://merganser.math.gvsu.edu/david/linear.algebra/ula/ula/ula.html) License: CC-BY Pretext Book
* [Linear Algebra, Theory And Applications by Kenneth Kuttler](https://open.umn.edu/opentextbooks/textbooks/linear-algebra-theory-and-applications) [PDF](https://resources.saylor.org/wwwresources/archived/site/wp-content/uploads/2012/02/Linear-Algebra-Kuttler-1-30-11-OTC.pdf) License: CC-BY
* [Linear Algebra for ML](https://ml-cheatsheet.readthedocs.io/en/latest/linear_algebra.html) License: MIT
* [Open Resources for Community College Algebra (ORCCA)](https://spaces.pcc.edu/pages/viewpage.action?pageId=52729944) or the [book](https://spot.pcc.edu/math/orcca/ed2/html/frontmatter.html) License: CC-BY Pretext Book
* [MATH 1220 Linear Algebra 1 by Michael Doob](https://linearalgebra.math.umanitoba.ca/math1220/) License: CC (?) Pretext Book
* [Elements of Linear and Multilinear Algebra by John M. Erdman](https://web.pdx.edu/~erdman/ELMA/) [PDF](https://web.pdx.edu/~erdman/ELMA/multilinear_algebra_pdf.pdf) License: CC-BY

## Book Recommendation

* [Amazon - Linear Algebra with Applications: Williams, Gareth: 9781284120097: Books](https://www.amazon.com/Linear-Algebra-Applications-Gareth-Williams/dp/1284120090)
* [Matrix Analysis & Applied Linear Algebra](http://matrixanalysis.com/)
* [Linear Algebra for Everyone, Gilbert Strang](https://math.mit.edu/~gs/everyone/)
* [Introduction to Linear Algebra (Gilbert Strang): Strang, Gilbert: 9780980232776: Amazon.com: Books](https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-Strang/dp/0980232775)
* [Linear Algebra: A Modern Introduction: Poole, David: 8601421990653: Books - Amazon](https://www.amazon.com/Linear-Algebra-Introduction-David-Poole/dp/1285463242)
* [Linear Algebra and Its Applications: Lay, David, Lay, Steven, McDonald, Judi: 9780321982384: Amazon.com: Books](https://www.amazon.com/Linear-Algebra-Its-Applications-5th/dp/032198238X)
* [Numerical Linear Algebra: Lloyd N. Trefethen, David Bau III: 8581000033141: Books: Amazon.com](https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefethen/dp/0898713617)
* [Linear Algebra: Step by Step: Singh, Kuldeep: 8601300149776: Books: Amazon.com](https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/0199654441)
* [No Bullshit Guide to Linear Algebra](https://minireference.gumroad.com/l/noBSLA)
* [Linear Algebra - Mathematics - MIT OpenCourseWare](https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/)
* [Free Linear Algebra textbook, from Jim Hefferon](https://hefferon.net/linearalgebra/index.html) CC-BY
* [Linear Algebra Done Wrong](https://www.math.brown.edu/streil/papers/LADW/) CC-BY
* [Introduction to Applied Linear Algebra–Vectors, Matrices, and Least Squares](https://web.stanford.edu/~boyd/vmls/)
* [Practical Linear Algebra: A Geometry Toolbox , Fourth Edition](http://www.farinhansford.com/books/pla/)
* [Linear Algebra - Mathematics - MIT OpenCourseWare](https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/)
* [Linear and Geometric Algebra](http://www.faculty.luther.edu/~macdonal/laga/)
* [Contents - 3D Math Primer for Graphics and Game Development](https://gamemath.com/book/)

## Video Recommendation

* [3Blue1Brown: Linear Alg - YouTube](https://www.youtube.com/playlist?list=PL0-GT3co4r2y2YErbmuJw2L5tW4Ew2O5B)
* [Essence of linear algebra - YouTube](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)
* [Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications - YouTube](https://www.youtube.com/playlist?list=PLlXfTHzgMRUKXD88IdzS14F4NxAZudSmv)

## Table of Contents some of the Open Books

### Interactive Linear Algebras by Dan Margalit

1. Systems of Linear Equations: Algebra (pp 1-27)
2. Systems of Linear Equations: Geometry (pp 29-112)
3. Linear Transformations and Matrix Algebra (pp 113-185)
4. Determinants (pp 187-235)
5. Eigenvalues and Eigenvectors (pp 237-337)
6. Orthogonality (pp 339-407)

### Discover Linear Algebra by Jeremy Sylvestre

1. Systems of Equations and Matrices (pp 7-169)
   * Systems of linear equations
   * Solving systems using matrices
   * Using systems of equations
   * Matrices and matrix operations
   * Matrix inverses
   * Elementary matrices
   * Special forms of square matrices
   * Determinants
   * Determinants versus row operations
   * Determinants, the adjoint, and inverses
2. Vector Spaces (pp 170-374)
   * Introduction to vectors
   * Geometry of vectors
   * Orthogonal vectors
   * Geometry of linear systems
   * Abstract vector spaces
   * Subspaces
   * Linear independence
   * Basis and Coordinates
   * Dimension
   * Column, row, and null spaces
3. Introduction to Matrix Forms (pp 375-413)
   * Eigenvalues and eigenvectors
   * Diagonalization

### Linear Algebra by Jim Hefferon

1. Linear Systems
   * Solving Linear Systems
   * Linear Geometry
   * Reduced Echelon Form
2. Vector Spaces
   * Definition of Vector Space
   * Linear Independence
   * Basis and Dimension
3. Maps Between Spaces
   * Isomorphisms
   * Homomorphisms
   * Computing Linear Maps
   * Matrix Operations
   * Change of Basis
   * Projection
4. Determinants
   * Definition
   * Geometry of Determinants
   * Laplace's Formula
5. Similarity
   * Complex Vector Spaces
   * Similarity
   * Nilpotence
   * Jordan Form

### A First Course in Linear Algebra by Robert A. Beezer

1. Systems of Linear Equations
2. Vectors
3. Matrices
4. Vector Spaces
5. Determinants
6. Eigenvalues
7. Linear Transformations
8. Representations

### Linear Algebra, Theory And Applications by Kenneth Kuttler

1. Preliminaries
2. Matrices and Linear Transformations
3. Determinants
4. Row Operations
5. Some Factorizations
6. Linear Programming
7. Spectral Theory
8. Vector Spaces and Fields
9. Linear Transformations
10. Linear Transformations Canonical Forms
11. Markov Chains and Migration Processes
12. Inner Product Spaces
13. Self Adjoint Operators
14. Norms for Finite Dimensional Vector Spaces
15. Numerical Methods for Finding Eigenvalues

### MATH 1220 Linear Algebra 1 by Michael Doob

1. Systems of Linear Equations
2. Matrix theory
3. The Determinant
4. Vectors in Euclidean n-space
5. Eigenvalues and eigenvectors
6. Linear transformations

## Markov Chains

* [Examples of Markov chains - Wikipedia](https://en.wikipedia.org/wiki/Examples_of_Markov_chains)
* [Math 22 - Linear Algebra with Applications](https://math.dartmouth.edu/~m22f19/project.php)
* [Markov Chains explained visually](https://setosa.io/ev/markov-chains/)
* [Visualizing a Markov Chain - Will Hipson](https://willhipson.netlify.app/post/markov-sim/markov_chain/)
* [Markov Chains](https://setosa.io/markov/index.html#%7B%22tm%22%3A%5B%5B0.5%2C0.5%5D%2C%5B0.5%2C0.5%5D%5D%7D)
* [rwet/ngrams-and-markov-chains.ipynb at master · aparrish/rwet](https://github.com/aparrish/rwet/blob/master/ngrams-and-markov-chains.ipynb)