College Level Advanced Linear Algebra! Theory & Programming!

Course Curriculum

Chapter 1: Introduction To The Course

Lecture 1: Welcome & Introduction !

Lecture 2: Prerequisites

Lecture 3: Exams, Written Scripts & Code Files

Chapter 2: Introduction To Matrices : Linear Independence And Matrix Multiplication

Lecture 1: Column Method For Matrix Vector Multiplication

Lecture 2: Linear Combinations And Independence – 1

Lecture 3: Linear Combinations And Independence – 2

Lecture 4: The Planes Picture vs The Vectors Picture

Lecture 5: Matrix Rank And Case Of Rectangular Matrices

Lecture 6: Row By Matrix Multiplication

Lecture 7: Matrix Matrix Multiplication – 1 – Dot Product Method

Lecture 8: Matrix Matrix Multiplication – 2 – Column Method

Lecture 9: Matrix Matrix Multiplication – 3 – Row Method

Lecture 10: Matrix Matrix Multiplication – 4 – Outer Product

Lecture 11: Matrix Matrix Multiplication – 5 – Block Multiplication

Chapter 3: Introduction To Gaussian Elimination And Matrix Inverse

Lecture 1: Introduction To Gaussian Elimination

Lecture 2: Gaussian Elimination With Row Exchange

Lecture 3: Elimination Using Matrices

Lecture 4: Row And Column Exchange Using Matrices

Lecture 5: Intuition Of Matrix Inverse

Lecture 6: Python Example & Matrix Inverse by Intuition

Lecture 7: Gauss-Jordan Inverse with proof

Lecture 8: Python, Matlab & Hand Example For Matrix Inverse

Lecture 9: Notes Regarding Inverses, Determinants, And Pseudo-Inverses

Chapter 4: Test Your Self ! – Exam 1 !

Lecture 1: Test Your Self ! – Exam 1 !

Chapter 5: The Computer Graphics Section !

Lecture 1: Introduction To Computer Graphics

Lecture 2: The Computer Graphics Pipeline

Lecture 3: Rotation By 90 Degrees Matrix in 2D

Lecture 4: Rotation By Arbitrary Angle Matrix In 2D

Lecture 5: Orthogonal Matrices And Their Inverses

Lecture 6: Rotation About The X-Axis in 3D

Lecture 7: The Scaling Matrix

Lecture 8: The Homogeneous Coordinates And Translation Matrices

Lecture 9: The Order Of Transformation Matters !

Lecture 10: Reflection Matrix Around The X-Axis

Lecture 11: Reflection Around Arbitrary Line in 2D – Method I

Lecture 12: Reflection Around Arbitrary Line In 2D – Method II

Lecture 13: Rotation About Arbitrary Axis in 3D – Method I

Lecture 14: Rotation About Arbitrary Axis In 3D – Method II

Lecture 15: Reflection Around Arbitrary Plane In 3D

Lecture 16: Rotations & Improper Rotations

Lecture 17: Notes About The Following Three Videos

Lecture 18: Mathematics Of The Camera – I

Lecture 19: Mathematics Of The Camera – II

Lecture 20: Mathematics Of The Camera – III

Lecture 21: Hierarchical Transformations And The Scene Graph

Chapter 6: The Robotics Section !

Lecture 1: Robotics And Change Of Reference Frames – I

Lecture 2: Robotics And Change Of Reference Frames II

Lecture 3: Robotics And Change Of Reference Frames III

Lecture 4: Matlab : Robotics And Change Of Reference Frames IV – Numerical Example in 2D

Lecture 5: Robotics And Change Of Reference Frames V – The 3D situation

Lecture 6: Robotics And Change Of Reference Frames VI – The Camera Matrix Revisited

Chapter 7: Test Your Self ! – Exam 2 !

Lecture 1: Test Your Self ! – Exam 2 !

Chapter 8: Test Your Self ! – Exam 3 !

Lecture 1: Test Your Self ! – Exam 3 !

Chapter 9: EigenValues & EigenVectors ( I ) : Introduction

Lecture 1: Introduction To EigenValues And EigenVectors

Lecture 2: EigenVs Geomteric Definition

Lecture 3: EigenVs – Intuitive Examples I

Lecture 4: EigenVs Intuitive Examples II

Lecture 5: EigenVs Formal Calculation

Lecture 6: EigenVs Numerical Examples – I

Lecture 7: EigenVs Numerical Examples – II

Lecture 8: Repeated EigenValues And Dependent EigenVectors

Lecture 9: The Rotation Matrix And Complex EigenVectors

Lecture 10: Proof : Different EigenValues have Independent EigenVectors

Lecture 11: Matrix Diagonalization Using Eigen Decomposition

Lecture 12: Complex EigenVs For Real Matrices Are Always Conjugate Pairs

Lecture 13: Matrix Powers & Eigen Decomposition

Lecture 14: Determinant Is The Product Of EigenValues

Chapter 10: EigenValues & EigenVectors ( II ) : Difference Equations

Lecture 1: Difference Equations & Eigen Decomposition

Lecture 2: Matlab : Visualization Of Difference Equations Solved Example

Lecture 3: Transforming Recurrence Relations To Matrix Form

Lecture 4: The Case Of Complex EigenVs & Difference Equations

Lecture 5: Matlab : Visualization Of Complex EigenVs And Difference Equations

Chapter 11: EigenValues & EigenVectors ( III ) : Differential Equations

Lecture 1: Systems Of Differential Equations

Lecture 2: The Matrix Exponential And Its Diagonalization

Lecture 3: Free Response Of A System Of Differential Equations – I

Lecture 4: Free Response Of A System Of Differential Equations – II

Lecture 5: Free Response Of A System Of Differential Equations – III

Lecture 6: Free Response – Solved Example – I

Lecture 7: Free Response – Solved Example – II

Lecture 8: Matlab : Visualization Of Free Response Of Systems Of Differential Equations

Lecture 9: Why Is It Called Free Response ?

Lecture 10: Forced Response Of Systems Of Differential Equations

Lecture 11: Forced Response – Solved Example

Lecture 12: Matab : Visualization Of Forced Response Of Systems Of Differential Equations

Lecture 13: Transforming Higher Order ODEs To Systems Of First Order ODEs

Chapter 12: Test Your Self ! – Exam 4 !

Lecture 1: Test Your Self ! – Exam 4 !

Chapter 13: Matrix Inverse Using Cofactors & The Cayley Hamilton Theorem

Lecture 1: The Cofactors Matrix And Adjoint Matrix