**Links and References**

**Books**

**Required Text:**Linear Algebra with Applications, 4th ed, Gilbert Strang (book review1 book review 2 by data scientist)

**Standard texts for a second course in Linear Algebra (no applications)**

A Second Course in Linear Algebra, Garcia and Horn

Linear Algebra in Action, Dym

Linear Algebra Done Right, Axler (free GT download) [determinant-free treatment with no applications]

Linear Algebra, Hoffman and Kuntz [mathematical treatment with no applications]

**Recommended texts for a first course in Linear Algebra**

Elementary Linear Algebra, Anton

Introduction to Linear Algebra, Strang

UCLA lecture notes, Tao

**Recommended text to study Functional Analysis (infinite dimensional linear algebra)**

Introductory Functional Analysis with Applications, Kreyszig

**Videos**

Strang video lectures from his first course on linear algebra and accompanying notes

Khan Academy (material from first course, provides computational exercises with feedback)

Essence of Linear Algebra

Interesting links

Too Much Calculus, Strang

The Language of Linear Algebra, Strang

Knill's linear algebra course handouts (very visual and application oriented)

Foundations of Data Science, book by Blum, Hopcroft, and Kannan

Good linear algebra problems (Kazdan)

Linear Algebra User's Manual (Moore)

Math, Numerics, and Programming for Mechanical Engineers

Necessary And Sufficient Conditions For Existence of the LU Factorization of an Arbitrary Matrix (Johnson and Okunev)

Proof of Gaussian elimination

Gaussian Elimination, LU-Factorization, Cholesky Factorization, Reduced Row Echelon Form

Chinese used Gaussian Elimination in 300-200 BC

The Gauss-Jordan elimination game

Counting Operations in Gaussian Elimination

The Fundamental Theorem of Linear Algebra, Strang

Transform a dog

Fat, Square and Thin Matrices - Number of Solutions to Systems of Linear Equations

Mathematica Demo: Approximation by Legendre polynomials

Mathematica Demo: Approximation by Fourier "polynomials"

From Bezier to Bernstein (Casselman)

Good video introduction to Be'zier curves

Vector space products, sums, and tensor products (Milson)

How to loose your fear of tensor products

Notes on tensor products

A geometric appraoch to determiants (Hannah)

Applications of determinants

A really short proof of Cramer's rule

Down with Determinants (Azler)

A summary of how the properties of different matrices are reflected in the eigenvalues/eigenvectors

Intuitive explanation of eigenvalues and eigenvectors for ballet dancers

Singularity and determinants of random matrices (Tao)

Solving cubic equations Solving quartic equations Quintic equations

Many real world applications of linear systems of ODEs

Dynamical models of love 1 2

Eigenvalues of AB and BA

Quantum computing and unitary matrices

Quantum computing: an introduction (Lecture by Jean Bellissard)

The Jordan canonical form made easy (actually not so easy)

Examples of JCF 1

Jordan Canonical Form of the Google Matrix

Proof of change of basis theorem

Nineteen Dubious Ways to Compute the Exponential of a Matrix

Excellent introduction to SVD with applications

Netflix collaborative prediction using singular value decomposition

Using singular value decomposition to compress an image of an allosaurus

What is the biological significance of the SVD?

Foundations of Data Science, book by Blum, Hopcroft, and Kannan (chapter 3 on SVD)

Matlab code to compress Lenna lenna.png

Quantum Mechanics in Simple Matrix Form (Dover Books on Physics), Thomas Jordan

Special relativity using linear algebra (Naslund)

Too Much Calculus, Strang

The Language of Linear Algebra, Strang

Knill's linear algebra course handouts (very visual and application oriented)

Foundations of Data Science, book by Blum, Hopcroft, and Kannan

Good linear algebra problems (Kazdan)

Linear Algebra User's Manual (Moore)

**Chapter 1**Math, Numerics, and Programming for Mechanical Engineers

Necessary And Sufficient Conditions For Existence of the LU Factorization of an Arbitrary Matrix (Johnson and Okunev)

Proof of Gaussian elimination

Gaussian Elimination, LU-Factorization, Cholesky Factorization, Reduced Row Echelon Form

Chinese used Gaussian Elimination in 300-200 BC

The Gauss-Jordan elimination game

Counting Operations in Gaussian Elimination

**Chapter 2**The Fundamental Theorem of Linear Algebra, Strang

Transform a dog

Fat, Square and Thin Matrices - Number of Solutions to Systems of Linear Equations

**Chapter 3**Mathematica Demo: Approximation by Legendre polynomials

Mathematica Demo: Approximation by Fourier "polynomials"

From Bezier to Bernstein (Casselman)

Good video introduction to Be'zier curves

Vector space products, sums, and tensor products (Milson)

How to loose your fear of tensor products

Notes on tensor products

**Chapter 4**A geometric appraoch to determiants (Hannah)

Applications of determinants

A really short proof of Cramer's rule

Down with Determinants (Azler)

**Chapter 5**A summary of how the properties of different matrices are reflected in the eigenvalues/eigenvectors

Intuitive explanation of eigenvalues and eigenvectors for ballet dancers

Singularity and determinants of random matrices (Tao)

Solving cubic equations Solving quartic equations Quintic equations

Many real world applications of linear systems of ODEs

Dynamical models of love 1 2

Eigenvalues of AB and BA

Quantum computing and unitary matrices

Quantum computing: an introduction (Lecture by Jean Bellissard)

The Jordan canonical form made easy (actually not so easy)

Examples of JCF 1

Jordan Canonical Form of the Google Matrix

Proof of change of basis theorem

Nineteen Dubious Ways to Compute the Exponential of a Matrix

**Chapter 6**Excellent introduction to SVD with applications

Netflix collaborative prediction using singular value decomposition

Using singular value decomposition to compress an image of an allosaurus

What is the biological significance of the SVD?

Foundations of Data Science, book by Blum, Hopcroft, and Kannan (chapter 3 on SVD)

Matlab code to compress Lenna lenna.png

**Applications**Quantum Mechanics in Simple Matrix Form (Dover Books on Physics), Thomas Jordan

Special relativity using linear algebra (Naslund)

**Software**

Matlab Linear Algebra Cheat Sheet 1

Matlab Linear Algebra Cheat Sheet 2

Matlab Linear Algebra Tutorial 1

Matlab Linear Algebra Tutorial 2

Matlab Linear Algebra Teaching Codes

Java (and other) Demos