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.
Overview
Syllabus
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.
Taught by
Linda Green
