Table of matrix functions
Listed below is a table of some common matrix functions, some of their application domains, and their corresponding NumPy/SciPy calls (under each respective linalg module).
| name | matrix function | Applications | NumPy/SciPy linalg call |
|---|---|---|---|
| identity | A | Basic matrix operations | A |
| log | \log(A) | Determinant, entropy-like measures | logm(A) |
| exp | e^A | Dynamical systems, graph diffusion | expm(A) |
| inv | A^{-1} | Stability analysis, linear systems | inv(A) |
| sign | \text{sgn}_\epsilon(A) | Rank approximation, low-rank modeling | U @ U.T |
| sqrt | A^{1/2} | Diffusion, kernel methods | sqrtm(A) |
| square | A^2 | Energy measures, stability | A @ A |
| topk | P_A (eigenspace) | Dim. reduction, feature extraction | Custom projection matrix |
| tikhonov | (A + \lambda I)^{-1} | Regularized inversion, stability | inv(A + c * eye(n)) |
| exp | e^{-tA} | Diffusion on graphs, spectral clustering | expm(-t * A) |
| pagerank | (I - \alpha A)^{-1}v | Network centrality, web ranking | Iterative solver |
If you know of another useful or commonly used matrix function, feel feel to make a PR to add it!