● Introduction to Linear Algebra
● Sets, Relations, Functions, and Fields
● Abstract Algebra
● Vectors and Vector Spaces
● Bases and Dimension
● Linear Transformations
● Matrix Representation
● Inverse of Matrix
● Linear Operations
● Elementary Matrix Operations
● Gaussian Elimination
● Triangular Factorization
● LDU Decomposition
● Orthogonal Complement
● Dual Spaces
● Linear Functional
● (Non) Homogeneous / General Solutions
● Determinant
● Diagonalizability
● Matrix Limits and Markov Chains
● Invariant Subspaces
● Euclidean/Unitary/Hermitian Spaces
● QR Decomposition
● Least Square Approximation
● Symmetric/Definite Matrices
● Normal/Self-Adjoint Operators
● Spectral Theorem
● Approximation and Extremal Points
● Singular Value Decomposition
● Congruent Transformation
● Generalized Eigenvalue Problem
● Conditioning and Rayleigh Quotient
● Vector/Matrix Norms
● Jordan Canonical Form
