Introduction To The Course
  • Welcome & Introduction !
  • Prerequisites
  • Exams, Written Scripts & Code Files
Introduction To Matrices : Linear Independence And Matrix Multiplication
  • 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 And Matrix Inverse
  • 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 !
  • Test Your Self ! - Exam 1 !
The Computer Graphics Section !
  • 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
The Robotics Section !
  • 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 2 !
Test Your Self ! - Exam 3 !
  • Test Your Self ! - Exam 3 !
EigenValues & EigenVectors ( I ) : Introduction
  • 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
EigenValues & EigenVectors ( II ) : Difference Equations
  • 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
EigenValues & EigenVectors ( III ) : Differential 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 !
  • Test Your Self ! - Exam 4 !
Matrix Inverse Using Cofactors & The Cayley Hamilton Theorem
  • The Cofactors Matrix And Adjoint Matrix