Matrix Algebra¶
- Introduction
- Linear independence, span, rank
- Invertible matrices
- Trace and determinant
- Unitary and orthogonal matrices
- Eigen values
- Singular values
- Matrix norms
- Norms like \(\ell_p\) on complex vector space
- Properties of Frobenius norm
- Consistency of a matrix norm
- Subordinate matrix norm
- Operator norm
- p-norm for matrices
- The 2-norm
- Unitary invariant norms
- More properties of operator norms
- Row column norms
- Block diagonally dominant matrices and generalized Gershgorin disc theorem
- Matrix Calculus