**Links and References**

**Books**

**Required Text:**Linear Algebra with Applications, 4th ed, Gilbert Strang (book review)

**Standard texts for a second course in Linear Algebra**

Linear Algebra Done Right, Axler (free GT download) [Mathematical and 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

Terrence Tao UCLA lecture notes

**Videos**

Strang video lectures from his first course on linear algebra

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

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 that matrix multiplication is associative (essential!)

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

The Fundamental Theorem of Linear Algebra, Strang

Transform a dog

From Bezier to Bernstein (Casselman)

A geometric approach to determinants (Hannah)

Applications of determinants

A really short proof of Cramer's rule

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)

Good video introduction to Be'zier curves

The Jordan canonical form made easy

Jordan Canonical Form of the Google Matrix

Proof of change of basis theorem

Special relativity using linear algebra (Naslund)

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

-----

Quick review of 2×2 matrices for ODEs (*)

Jordan Canonical Form for 2D matrices (*)

Solving 2x2 systems of ODEs (*)

Phase portraits of 2x2 systems of linear ODEs (summary) (*)

Phase portraits of 2x2 systems of linear ODEs (details) (*)

Invertible 2x2 matrices map unit circle to ellipse another proof another proof

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

**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 that matrix multiplication is associative (essential!)

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

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

Transform a dog

**Chapter 3**From Bezier to Bernstein (Casselman)

**Chapter 4**A geometric approach to determinants (Hannah)

Applications of determinants

A really short proof of Cramer's rule

**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)

Good video introduction to Be'zier curves

The Jordan canonical form made easy

Jordan Canonical Form of the Google Matrix

Proof of change of basis theorem

Special relativity using linear algebra (Naslund)

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

-----

**Links on Linear Systems of ODEs from Math 4541**Quick review of 2×2 matrices for ODEs (*)

Jordan Canonical Form for 2D matrices (*)

Solving 2x2 systems of ODEs (*)

Phase portraits of 2x2 systems of linear ODEs (summary) (*)

Phase portraits of 2x2 systems of linear ODEs (details) (*)

Invertible 2x2 matrices map unit circle to ellipse another proof another proof