1. Linear equations
2. Matrix theory
- vector
- matrix
- matrix addition
- matrix scalar addition
- matrix multiplication
- zero matrix
- identity matrix
- inverse matrixes
- determinant
- transpose
- conjugate transpose
- symmetric matrix
- hermitian matrix
- orthonormal matrix
- unitary matrix
- GL(n) group
- O(n) group
- SO(n) group
3. Linear spaces
- linear space
- linear subspace
- linear isomorphism
- linear span
- basis (linear space)
- basis dimension
- orthogonality
- inner product
- projection
- gram-schmitt process
- orthonormal basis
- Euclidean space
- Cauchy-Schwarz inequality
- Triangle inequality
4. Linear maps
- kernel
- image
- column space
- row space
- rank
- rank-nullity theorem
- kernel space
- image
5. Bilinear maps
6. Eigenequations
7. Multilinear algebra