Vectors & Matrices

Introduction to Vectors

Vector Operations

Introduction to Matrices

Matrix Multiplication

Dot and Cross Products

Lines and Planes in 3D Space

Solving Systems of Linear Equations

Matrix Inverse and Determinants

Orthogonality and Projections onto Subspaces

Vector Spaces and Subspaces

Basis, Dimension, and Rank

Linear Transformations

Eigenvalues and Eigenvectors

Quadratic Forms and Conic Sections

Diagonalization and the Spectral Theorem

Singular Value Decomposition (SVD)

LU and QR Decompositions

Principal Component Analysis (PCA)

Introduction to Tensors and Multilinear Algebra