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.