Linear Algebra

Explore the fundamental concepts of linear algebra in this comprehensive 3.5-hour video tutorial. Delve into the world of matrices, vector spaces, and abstract mathematical concepts that build upon calculus. Learn about systems of linear equations, matrix operations, determinants, vector cross products, and inverse matrices. Discover vector spaces, subspaces, linear independence, and basis. Investigate linear transformations, orthogonality, and the Gram-Schmidt process. Master eigenvalues, eigenvectors, and diagonalization. Conclude with an introduction to complex, Hermitian, and unitary matrices. Gain a solid foundation in linear algebra and its wide-ranging applications through clear explanations and examples.

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.