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Linear Equations Introduction

Solving Systems of Linear Equations

Using Matrices to Solve Systems of Linear Equations

Reduced Row Echelon Form

Gaussian Elimination

Existence and Uniqueness of Solutions

Linear Equations Setup

Matrix Addition and Scalar Multiplication

Matrix Multiplication

Properties of Matrix Multiplication

Interpretations of Matrix Multiplication

Introduction to Vectors (Math 210)

Solving Vector Equations

Solving Matrix Equations

Matrix Inverses

Matrix Inverses for 2x2 Matrices

Equivalent Conditions for a Matrix to be Invertible

Properties of Matrix Inverses

Transpose

Symmetric and Skew-symmetric Matrices

Trace

The Determinant of a Matrix

Determinant and Elementary Row Operations

Determinant Properties.

Invertible Matrices and Their Determinants

Eigenvalues and Eigenvectors

Properties of Eigenvalues

Diagonalizing Matrices

Dot Product (Linear Algebra)

Unit Vectors

Orthogonal Vectors

Orthogonal Matrices

Symmetric Matrices and Eigenvectors and Eigenvalues

Symmetric Matrices and Eigenvalues and Eigenvectors - Proofs

Diagonalizing Symmetric Matrices

Linearly Independent Vectors

Gram-Schmidt Orthogonalization

Singular Value Decomposition - Introduction

Singular Value Decomposition - How To Find It

Singular Value Decomposition - Why It Works

Description:

Dive into a comprehensive 7-hour course on Linear Algebra, covering essential topics from linear equations to advanced matrix operations. Master solving systems of linear equations, Gaussian elimination, and matrix multiplication. Explore vector operations, determinants, eigenvalues, and eigenvectors. Learn about orthogonality, Gram-Schmidt orthogonalization, and the Singular Value Decomposition. Gain a solid foundation in linear algebra concepts and techniques applicable to various fields of mathematics and science.

Linear Algebra

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#Mathematics #Algebra #Linear Algebra #Gaussian Elimination #Matrix Operations #Determinants #Singular Value Decomposition #Symmetric Matrices