# Advanced Matrix Theory and Linear Algebra for Engineers

## Video Lectures

Displaying all 40 video lectures.
I. Introduction to Matrix Theory
Lecture 1

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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

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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

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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

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Linear Systems Part 1
Lecture 5

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Linear Systems Part 2
Lecture 6

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Linear Systems Part 3
Lecture 7

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Linear Systems Part 4
III. Solutions of Linear Systems
Lecture 8

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Vector Spaces Part 1
Lecture 9

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Vector Spaces Part 2
Lecture 10

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Linear Independence and Subspaces Part 1
Lecture 11

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Linear Independence and Subspaces Part 2
Lecture 12

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Linear Independence and Subspaces Part 3
Lecture 13

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Linear Independence and Subspaces Part 4
Lecture 14

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Basis Part 1
Lecture 15

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Basis Part 2
Lecture 16

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Basis Part 3
Lecture 17

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Linear Transformations Part 1
Lecture 18

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Linear Transformations Part 2
Lecture 19

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Linear Transformations Part 3
Lecture 20

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Linear Transformations Part 4
Lecture 21

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Linear Transformations Part 5
Lecture 22

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Inner Product and Orthogonality Part 1
Lecture 23

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Inner Product and Orthogonality Part 2
Lecture 24

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Inner Product and Orthogonality Part 3
Lecture 25

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Inner Product and Orthogonality Part 4
Lecture 26

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Inner Product and Orthogonality Part 5
Lecture 27

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Inner Product and Orthogonality Part 6
Lecture 28

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Diagonalization Part 1
Lecture 29

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Diagonalization Part 2
Lecture 30

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Diagonalization Part 3
Lecture 31

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Diagonalization Part 4
Lecture 32

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Hermitian and Symmetric matrices Part 1
Lecture 33

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Hermitian and Symmetric matrices Part 2
Lecture 34

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Hermitian and Symmetric matrices Part 3
Lecture 35

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Hermitian and Symmetric matrices Part 4
Lecture 36

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Singular Value Decomposition (SVD) Part 1
Lecture 37

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Singular Value Decomposition (SVD) Part 2
Lecture 38

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Back To Linear Systems Part 1
Lecture 39

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Back To Linear Systems Part 2
Lecture 40

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Epilogue