VECTORS
- Vectors ✔
- Sets of Vectors
- Adding Vectors ✔
- Norms ✔
- Inner Products ✔
- Orthogonality ✔
- Projections ✔
- Outer Products ✔
- High dimensional ✔
MATRICES
- Linear combinations ✔
- Convex combinations ✔
- Matrices ✔
- Linear Transforms of Sets ✔
- Column & Row Geometry ✔
- Transposes ✔
- Matrix addition ✔
- Matrix multiplication ✔
- Matrix Norms ✔
- Block Matrix Structures ✔
BASES & COORDINATES
- Bases & Coordinates ✔
- Coordinate Transforms ✔
- Orthonormal Transforms ✔
- Inverses ✔
- Degrees of Invertibility
- Similarity Transforms ✔
- Congruent Transforms
- Orthonormalization ✔
- Gram-Schmidt Process ✔
RANGE & NULLSPACE
- Range
- Nullspace ✔
- Rank & Rank-Nullity ✔
- Fundamental Thm
SYSTEMS OF EQUATIONS
- Unique Solution (Square Matrix)
- Least Squares (Tall Matrix)
- Minimum Norm (Fat Matrix)
- Pseudo-inverses ✔
- Left \& Right Inverses ✔
- Elementary Matrices
- Gaussian Elimination ✔
- Householder Transformations
SUBSPACES & AFFINE SPACES
- Subspaces 1: Range Rep.
- Affine Spaces 1: Range Rep.
- Subspaces 2: Nullspace Rep.
- Affine Spaces 2: Nullspace Rep.
MATRIX METRICS
- Determinants
- Traces
EIGEN-PROBLEM
- Eigen-Problem: Intuitions
- Characteristic polynomial...
- Eigenvalues & vectors...
- 2x2 Matrix Eigenstructure
- 3x3 Matrix Eigenstructure
- Complex Eigenvalues
- Diagonalization
- Eigenvalue Multiplicity
- Nilpotent Matrices
- Jordan form
- Block Diagonalization
FUNCTIONS OF MATRICES
- Spectral Mapping Theorem
- Matrix Exponential
- Cayley Hamilton
BASIC MATRIX TYPES
- Diagonal
- Symmetric
- Skew-Symmetric
- Rotations
- Triangular
- Nilpotent
QUADRATIC FORMS
- Quadratic Forms
- Definite Matrices
MATRIX SHAPES
- Sym + Skew-Sym
- Shape Matrices (Grammians)
- Polar Decomposition
- Singular Value Decomposition
OTHER DECOMPOSITIONS
- LU Decompositions
- QR Decompositions