Visual Guides

The complex plane, binomial and polar form, Euler's formula, and conjugates.

Vector space axioms, subspaces, span, linear independence, basis, and dimension.

Matrix representations, kernel and image, injectivity and surjectivity, change of basis, and composition.

Dot products and norms, orthogonal sets and complements, projections, Gram-Schmidt, and orthogonal matrices.

Eigenvalues and eigenvectors, the characteristic equation, diagonalizability, and diagonalization of symmetric matrices.

Extending diagonalization to any matrix: singular values, the U, Sigma, V factorization, and its applications.