Linear Systems and Gaussian Elimination-Introduction
Introduction to the Course
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Linear System and Definition
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Three Solution Options and Coordinate System Visualization
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Linear Systems and Gaussian Elimination-Matrices and Gaussian Elimination
Linear System -> Matrix (Coefficient and Augmented)
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Rules of G.E. and Solving a Linear System
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G.E. Intuition and Simple Example
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G.E Example - Single Solution Part 1
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G.E Example - Single Solution Part 2
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G.E Example - Single Solution Part 3 + Meaning
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Linear Systems and Gaussian Elimination-Advanced G.E. with Examples
G.E. Example - Infinite Solutions
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G.E. Example - No Solutions
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G.E. Advanced Example - Part 1
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G.E. Advanced Example - Part 2
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Matrix Algebra-Introduction to Matrix Algebra + Sum + Scale
Matrix Algebra Sum
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Matrix Algebra Scale + Identity Overview
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Matrix Algebra-Matrix Multiplication
Matrix Multiplication + Small Example
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Matrix Multiplication - General Rules
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Matrix Multiplication Example
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Identity Matrix + Example
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Properties of a Linear System-Vectors and Linear Combinations
Introduction to Vectors + Coordinates
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Introduction to Linear Combinations
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Linear Combinations
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Linear Combinations Example
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Properties of a Linear System-Linear Independence
Span
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Span Example
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Ax = b
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Linear Independence
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Linear Independence Example Part 1
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Linear Independence Example Part 2
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Columns of a Matrix Being Linearly Independent
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Properties of a Linear System-Linear Transformations and Matrix Inverse
Linear Transformations
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Linear Transformations Example
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Matrix Inverse
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Matrix Inverse Example
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Determinant and Eigens-Determinants
Determinant Intro and 2x2 Example
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Inverse of 2x2 Matrix - Quick Method
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Determinant of 3x3 Matrix - Overview
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Determinant of 3x3 Matrix - Example with 1st Row
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Determinant of 3x3 Matrix - Example with 2nd Row
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Determinant and Eigens-Eigenvalues and Eigenvectors
Eigenvalue and Eigenvector - Overview
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Finding Eigenvector if Given Eigenvalue
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Characteristic Polynomic - Finding Eigenvalues
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Projections and Least Squares-Important Final Concepts
Transpose and Inner (Dot) Product
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Norm (Length) of a Vector
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Unit Vector Creation
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Distance Between Two Vectors
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Projections and Least Squares-Orthogonality, Projections and Least Squares
Orthogonal Vectors
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Orthogonal Projections Part I
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Orthogonal Projections Part II
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Least Squares Overview
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Least Squares Example
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