Linear Algebra
- Set, relation, function
- Vector space
- Linear combination and independence
- Metric, norm, and inner product spaces
- Column and null subspaces
- Orthogonality and projection vector
- Matrix, famous types, and matrix operations
- Solving a system of linear equations in special case
- Inverse of a matrix
- Determinant and its computational methods
- Eigenvalues and eigenvectors
- Spectral and Cholesky decompositions
- Rank of matrix
- Solving a system of linear equations in general case
- Singular values and singular vectors
- Singular value decomposition
- pseudoinverse
- Positive semidefinite matrix
- An introduction to software
- Optional content (similar matrix, Schur complement theorem, vector and matrix norms, numerical methods)