**Links and References**

**Books**

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

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

A Second Course in Linear Algebra, Garcia and Horn

Linear Algebra Done Right, Axler (free GT download) [determinant-free treatment]

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

**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

QnAs with Gilbert Strang

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

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

Knill's Linear Algebra and ODE notes

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 Fundamental Theorem of Linear Algebra, Strang

Transform a dog

Mathematica Demo: Approximation by Legendre polynomials

Mathematica Demo: Approximation by Fourier "polynomials"

Computational complexity to evaluate determination different ways

A geometric approach to determiants (Hannah)

Applications of determinants

A really short proof of Cramer's rule

Examples of systems of linear ODEs

Leslie population model (old, but good)

Leslie population model slides

Great into to quantum computing by Prof. Jean Bellissard

**The many applications of linear algebra, Knill**Too Much Calculus, Strang

The Language of Linear Algebra, Strang

QnAs with Gilbert Strang

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

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

Knill's Linear Algebra and ODE notes

**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

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

Transform a dog

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

Mathematica Demo: Approximation by Fourier "polynomials"

**Chapter 4**Computational complexity to evaluate determination different ways

A geometric approach to determiants (Hannah)

Applications of determinants

A really short proof of Cramer's rule

**Chapter 5**Examples of systems of linear ODEs

Leslie population model (old, but good)

Leslie population model slides

******Chapter 6**Great into to quantum computing by Prof. Jean Bellissard