Linear Algebra and Fourier Analysis

System of Linear Equations [PSD]

Row-Echelon Form of Matrix [PSD]

Gaussian Elimination Method (Row Echelon Form) [PSD]

Gauss-Jordan Method (Reduced Row Echelon Form) [PSD]

Consistency Analysis, Row & Column Picture, Application of Linear System [PSD]

System Solve using Inverse Matrix, Elementary Matrix [PSD]

Gaussian Elimination - Quick Recap [EMNH]

Consistency Analysis, Application of Linear System, Intro to Inverse Matrix [RSQT]

Inverse Matrix, Elementary Matrix [RSQT]

Course Introduction [AAI]

Revisiting Matrices [AAI]

Introduction to Systems of Linear Equations [AAI]

System of Linear Equations as Linear Combinations of Vectors [AAI]

Solvability and Number of Solutions [AAI]

Linear Combination, Independence and Dependence [PSD]

Linear Combination, Linear Dependence, Linear Span - Part 1 [RSQT]

Linear Combination, Linear Dependence, Linear Span - Part 2 [RSQT]

Spanning Sets, Linear Independence and Dependence [MHM]

Revisiting Vectors [AAI]

Intro to Linear Combination [AAI]

Vectors of R^n [AAI]

Introduction to Linear Combination (Part 2) [AAI]

Binary Operation [PSD]

Group and Field [PSD]

General Vector Spaces - Part 1 [PSD]

General Vector Spaces - Part 2 (Advanced) [PSD]

Linear Subspaces - Part 1 [PSD]

Linear Subspaces - Part 2 (Advanced) [PSD]

Linear Span, Basis and Dimension - Part 1 [PSD]

Basis and Dimension - Part 2 (Advanced) [PSD]

Four Fundamental Subspaces (Row, Column, Null, Left Null Space) [PSD]

Span and Basis - Quick Recap [EMNH]

Null Space, Row Space and Column Space - Quick Recap [EMNH]

Examples for Verifying a Subspace - Part 1 [EMNH]

More Examples on Subspace and Span of R^4 - Part 2 [EMNH]

Row Space, Column Space and Null Space [EMNH]

Finding Nullity and Rank of a Matrix - Part 3 [EMNH]

Span and Basis [EMNH]

Vector Spaces - Part 1 [RSQT]

Vector Spaces - Part 2 (Segment 1) [RSQT]

Vector Spaces - Part 2 (Segment 2) [RSQT]

Vector Spaces [RSQT]

Basis and Dimension [RSQT]

Four Fundamental Spaces [RSQT]

Vectors in R^n [MHM]

Vector Spaces [MHM]

Subspaces and Linear Combinations [MHM]

Basis and Dimension of Vector Spaces [MHM]

Row Space, Column Space and Rank of a Matrix [MHM]

Coordinates and Change of Basis - Part 1 [MHM]

Coordinates and Change of Basis - Part 2 [MHM]

Coordinates and Alternative Coordinates with Respect to Basis Vectors [AAI]

The Four Fundamental Subspaces - Part 1 [AAI]

The Four Fundamental Subspaces - Part 2 [AAI]

Linear Transformations [PSD]

Image and Kernel of a Linear Transformation [PSD]

Linear Transformation (Advanced) [PSD]

Linear Transformation - Linearity, Kernel, Image (Quick Recap) [EMNH]

Kernel and Image of a Transformation - Part 4 [EMNH]

Linear Transformation - Math Examples [EMNH]

Kernel - Part 1 [RSQT]

Kernel - Part 2 [RSQT]

Linear Transformation - Part 3 [RSQT]

Matrix Transformation - Part 1 [AAI]

Matrix Transformation - Part 2 [AAI]

Fun with Transformations [AAI]

Problem Solving Discussion: Linear Transformations [AAI]

Eigenvalue [PSD]

Eigenvector [PSD]

Diagonalization [PSD]

Diagonalization [RSQT]

Diagonalization Visualized [AAI]

Inner Product [PSD]

Orthogonality in Inner Product Space [PSD]

Orthogonal Basis and Gram-Schmidt Procedure [PSD]

Inner Product, Length and Orthogonality [EMNH]

Orthogonal Set, Gram-Schmidt Process [EMNH]

Orthogonal Basis, Basics of Fourier Series [EMNH]

Inner Product [RSQT]

Orthogonality [RSQT]

Orthogonal Complement and Gram-Schmidt [RSQT]

Orthogonal and Orthonormal Basis [AAI]

The Gram-Schmidt Process [AAI]

Least Square Method [AAI]

Finding the Best Fit Line [AAI]

Vector Projection - Part 1 [AAI]

Vector Projection - Part 2 [AAI]

Vector Projection - Part 3 [AAI]

Fourier Analysis: Physical Intuition (Series & Transform) [PSD]

Periodic Functions, Even and Odd Functions [PSD]

General Fourier Series [PSD]

Even and Odd Cases of Fourier Series [PSD]

Half Range Fourier Series (Sine & Cosine) [PSD]

Series Sum using Fourier Series and Parseval's Identity [PSD]

Complex Fourier Series [PSD]

Fourier Analysis - Part 1 [EMNH]

Fourier Analysis - Part 2 [EMNH]

Formula of the Fourier Series using the Inner Product [EMNH]

Common Mistakes in Fourier Series [EMNH]

Periodic Functions [EMNH]

Fourier Series - Part 1 [RSQT]

Fourier Series - Part 2 [RSQT]

Fourier Series - Part 3 [RSQT]

Fourier Sine and Cosine Series [RSQT]

Parseval's Identity [RSQT]

General Fourier Transformation (Fourier Integral) [PSD]

Fourier Cosine and Sine Transform [PSD]

Fourier Transformation - Quick Recap [EMNH]

Fourier Sine/Cosine Transformation - Quick Recap [EMNH]

Fourier Transform [RSQT]

Fourier Sine and Cosine Transform - Part 1 [RSQT]

Fourier Sine and Cosine Transform - Part 2 [RSQT]

Final Exam Guideline [PSD]

Final Review (Practice Sheet) [EMNH]

Weekly Wrap-Up - Week 1 [AAI]

Weekly Wrap-Up - Week 2 (Part 1) [AAI]

Weekly Wrap-Up - Week 2 (Part 2) [AAI]

Weekly Wrap-Up - Week 3 (Part 1) [AAI]

Weekly Wrap-Up - Week 3 (Part 2) [AAI]

Weekly Wrap-Up - Week 4 [AAI]

Weekly Wrap-Up - Week 5 [AAI]

Weekly Wrap-Up - Week 6 (Part 2) [AAI]

Weekly Wrap-Up - Week 6 (Part 1) [AAI]

Weekly Wrap-Up - Week 7 [AAI]

Weekly Wrap-Up - Week 9 (Part 1) [AAI]

Weekly Wrap-Up - Week 9 (Part 2) [AAI]