Overview
Syllabus
Introduction to Linear Algebra: Systems of Linear Equations.
Understanding Matrices and Matrix Notation.
Manipulating Matrices: Elementary Row Operations and Gauss-Jordan Elimination.
Types of Matrices and Matrix Addition.
Matrix Multiplication and Associated Properties.
Evaluating the Determinant of a Matrix.
The Vector Cross Product.
Inverse Matrices and Their Properties.
Solving Systems Using Cramer's Rule.
Understanding Vector Spaces.
Subspaces and Span.
Linear Independence.
Basis and Dimension.
Change of Basis.
Linear Transformations on Vector Spaces.
Image and Kernel.
Orthogonality and Orthonormality.
The Gram-Schmidt Process.
Finding Eigenvalues and Eigenvectors.
Diagonalization.
Complex, Hermitian, and Unitary Matrices.
Taught by
Professor Dave Explains