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!