Computation Complexity

1. Matrix multiplication
Matrix A (n x p , Matrix B (p x m): O(mnp)
2. Rank of matrix
- Use SVD (see SVD)
3. SVD Decomposition
Matrix m x n
\[
A = UDV^T
\]
Calculate U, D, V: $4m^2n + 8mn^2 + 9n^3$
Calculate V: $4mn^2 + 8 n^3$
Source [1]
4. Eigenvector decomposition
Matrix $m \times n$
Complexity: $m \times n \times min(m, n)$
Source [1 page 8]
5. Complexity of basic operators
Wikipedia