I. Introduction to Matrix Theory 
Lecture 1 Play Video 
Systems of Linear Equations Topics in this module: 1. First Basic Problem – Systems of Linear equations  Matrix Notation – The various questions that arise with a system of linear equations 2. Second Basic Problem – Diagonalization of a square matrix – The various questions that arise with diagonalization 
Lecture 2 Play Video 
Matrix Notation Topics in this module: 1. First Basic Problem – Systems of Linear equations  Matrix Notation – The various questions that arise with a system of linear equations 2. Second Basic Problem – Diagonalization of a square matrix – The various questions that arise with diagonalization 
Lecture 3 Play Video 
Diagonalization of a Square Matrix Topics in this module: 1. First Basic Problem – Systems of Linear equations  Matrix Notation – The various questions that arise with a system of linear equations 2. Second Basic Problem – Diagonalization of a square matrix – The various questions that arise with diagonalization 
II. Vector Spaces 
Lecture 4 Play Video 
Linear Systems Part 1

Lecture 5 Play Video 
Linear Systems Part 2

Lecture 6 Play Video 
Linear Systems Part 3

Lecture 7 Play Video 
Linear Systems Part 4

III. Solutions of Linear Systems 
Lecture 8 Play Video 
Vector Spaces Part 1

Lecture 9 Play Video 
Vector Spaces Part 2

Lecture 10 Play Video 
Linear Independence and Subspaces Part 1

Lecture 11 Play Video 
Linear Independence and Subspaces Part 2

Lecture 12 Play Video 
Linear Independence and Subspaces Part 3

Lecture 13 Play Video 
Linear Independence and Subspaces Part 4

Lecture 14 Play Video 
Basis Part 1

Lecture 15 Play Video 
Basis Part 2

Lecture 16 Play Video 
Basis Part 3

Lecture 17 Play Video 
Linear Transformations Part 1

Lecture 18 Play Video 
Linear Transformations Part 2

Lecture 19 Play Video 
Linear Transformations Part 3

Lecture 20 Play Video 
Linear Transformations Part 4

Lecture 21 Play Video 
Linear Transformations Part 5

Lecture 22 Play Video 
Inner Product and Orthogonality Part 1

Lecture 23 Play Video 
Inner Product and Orthogonality Part 2

Lecture 24 Play Video 
Inner Product and Orthogonality Part 3

Lecture 25 Play Video 
Inner Product and Orthogonality Part 4

Lecture 26 Play Video 
Inner Product and Orthogonality Part 5

Lecture 27 Play Video 
Inner Product and Orthogonality Part 6

Lecture 28 Play Video 
Diagonalization Part 1

Lecture 29 Play Video 
Diagonalization Part 2

Lecture 30 Play Video 
Diagonalization Part 3

Lecture 31 Play Video 
Diagonalization Part 4

Lecture 32 Play Video 
Hermitian and Symmetric matrices Part 1

Lecture 33 Play Video 
Hermitian and Symmetric matrices Part 2

Lecture 34 Play Video 
Hermitian and Symmetric matrices Part 3

Lecture 35 Play Video 
Hermitian and Symmetric matrices Part 4

Lecture 36 Play Video 
Singular Value Decomposition (SVD) Part 1

Lecture 37 Play Video 
Singular Value Decomposition (SVD) Part 2

Lecture 38 Play Video 
Back To Linear Systems Part 1

Lecture 39 Play Video 
Back To Linear Systems Part 2

Lecture 40 Play Video 
Epilogue
