Lectures related to Determinant, Area, and Volume

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Covers orthogonal bases, Gram-Schmidt method, linear independence, and orthonormal matrices in vector spaces.

Covers the basics of matrix inversion, properties of matrix multiplication, and the uniqueness of matrix inverses.

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Covers the concept of inverse matrices and systems resolution, including the conditions for matrix invertibility and the Gauss-Jordan algorithm.