MATH 2940

Basics

• Systems of Equations
• Matrices
• Row Operations
• Echelon Form
• Linear System Theorems
• Vectors
• Span

Matrix Algebra

• Matrix-Vector Product
• Homogeneous Systems
• Matrix Multiplication
• Identity Matrix
• Inverse Matrix
• Transpose
• Elementary Matrix
• [Linear Independence]
• [Transformations]
• [Linear Transformations]

Determinants

• [Determinants]
• [Determinant Rules]
• [Cofactor Method]
• [Cramer’s Rule]

Vector Space

• [Vector Spaces and Subspaces]
• [Null Spaces]
• [Column and Row Spaces]
• [Basis]
• Change of Coordinates
• [The Characteristic Polynomial]

Eigenvalues

• [Eigenvalues]
• [Multiplicity]
• Diagonalization
• [Dimension]
• [Markov Chains]
• [Stochastic Matrix]
• Steady State
• [Dot Product]
• [Distance and Magnitude]

Orthogonality

• Orthogonality
• [Orthogonal Projection]
• [Orthogonal and Orthonormal Sets]
• [Gram-Schmidt Process]
• [QR Decomposition]
• [Least-Squares]
• [Inner Product]

Symmetric Matrices

• [Spectral Decomposition]
• [Quadratic Form]
• Singular Value Decomposition