Lectures related to Column Rank and Systems of Equations

Introduces the concept of basis and canonical basis in linear algebra, essential for vector space representation.

Covers the Factorisation QR theorem and the Gram-Schmidt method for orthonormal bases.

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Covers the concept of change of basis matrix and its calculation through examples.

Covers echelon matrices, vector equations, linear combinations, and vector spans in R^n.

Covers the algorithm for matrix decomposition and base change in linear algebra.