Learning

Linear Transformations and Their Matrix Representations

Vector Spaces → Eigenvalues and Eigenvectors

This path provides a rigorous, university-level introduction to linear transformations, their properties, and their representation as matrices. Starting from vector spaces and linear maps, it progresses through kernels, images, rank-nullity, matrix representations, change of basis, invertibility, and isomorphisms, culminating in applications to solving linear systems and diagonalization.