- Welcome & Introduction !
- Prerequisites
- Exams, Written Scripts & Code Files
- Column Method For Matrix Vector Multiplication
- Linear Combinations And Independence - 1
- Linear Combinations And Independence - 2
- The Planes Picture vs The Vectors Picture
- Matrix Rank And Case Of Rectangular Matrices
- Row By Matrix Multiplication
- Matrix Matrix Multiplication - 1 - Dot Product Method
- Matrix Matrix Multiplication - 2 - Column Method
- Matrix Matrix Multiplication - 3 - Row Method
- Matrix Matrix Multiplication - 4 - Outer Product
- Matrix Matrix Multiplication - 5 - Block Multiplication
- Introduction To Gaussian Elimination
- Gaussian Elimination With Row Exchange
- Elimination Using Matrices
- Row And Column Exchange Using Matrices
- Intuition Of Matrix Inverse
- Python Example & Matrix Inverse by Intuition
- Gauss-Jordan Inverse with proof
- Python, Matlab & Hand Example For Matrix Inverse
- Notes Regarding Inverses, Determinants, And Pseudo-Inverses
- Test Your Self ! - Exam 1 !
- Introduction To Computer Graphics
- The Computer Graphics Pipeline
- Rotation By 90 Degrees Matrix in 2D
- Rotation By Arbitrary Angle Matrix In 2D
- Orthogonal Matrices And Their Inverses
- Rotation About The X-Axis in 3D
- The Scaling Matrix
- The Homogeneous Coordinates And Translation Matrices
- The Order Of Transformation Matters !
- Reflection Matrix Around The X-Axis
- Reflection Around Arbitrary Line in 2D - Method I
- Reflection Around Arbitrary Line In 2D - Method II
- Rotation About Arbitrary Axis in 3D - Method I
- Rotation About Arbitrary Axis In 3D - Method II
- Reflection Around Arbitrary Plane In 3D
- Rotations & Improper Rotations
- Notes About The Following Three Videos
- Mathematics Of The Camera - I
- Mathematics Of The Camera - II
- Mathematics Of The Camera - III
- Hierarchical Transformations And The Scene Graph
- Robotics And Change Of Reference Frames - I
- Robotics And Change Of Reference Frames II
- Robotics And Change Of Reference Frames III
- Matlab : Robotics And Change Of Reference Frames IV - Numerical Example in 2D
- Robotics And Change Of Reference Frames V - The 3D situation
- Robotics And Change Of Reference Frames VI - The Camera Matrix Revisited
- Test Your Self ! - Exam 2 !
- Test Your Self ! - Exam 3 !
- Introduction To EigenValues And EigenVectors
- EigenVs Geomteric Definition
- EigenVs - Intuitive Examples I
- EigenVs Intuitive Examples II
- EigenVs Formal Calculation
- EigenVs Numerical Examples - I
- EigenVs Numerical Examples - II
- Repeated EigenValues And Dependent EigenVectors
- The Rotation Matrix And Complex EigenVectors
- Proof : Different EigenValues have Independent EigenVectors
- Matrix Diagonalization Using Eigen Decomposition
- Complex EigenVs For Real Matrices Are Always Conjugate Pairs
- Matrix Powers & Eigen Decomposition
- Determinant Is The Product Of EigenValues
- Difference Equations & Eigen Decomposition
- Matlab : Visualization Of Difference Equations Solved Example
- Transforming Recurrence Relations To Matrix Form
- The Case Of Complex EigenVs & Difference Equations
- Matlab : Visualization Of Complex EigenVs And Difference Equations
- Systems Of Differential Equations
- The Matrix Exponential And Its Diagonalization
- Free Response Of A System Of Differential Equations - I
- Free Response Of A System Of Differential Equations - II
- Free Response Of A System Of Differential Equations - III
- Free Response - Solved Example - I
- Free Response - Solved Example - II
- Matlab : Visualization Of Free Response Of Systems Of Differential Equations
- Why Is It Called Free Response ?
- Forced Response Of Systems Of Differential Equations
- Forced Response - Solved Example
- Matab : Visualization Of Forced Response Of Systems Of Differential Equations
- Transforming Higher Order ODEs To Systems Of First Order ODEs
- Test Your Self ! - Exam 4 !
- The Cofactors Matrix And Adjoint Matrix