# hyperlearn.linalg

The linalg module contains all mathematical methods, decompositions and mirrors both Numpy’s linalg and Scipy’s linalg modules. HyperLearn’s modules are all optimized and I also showcase some novel new algorithms.

## Matrix Decompositions

Cholesky Decomposition | cholesky(X, [alpha]) | :math:`X=UsigmaV^T | Symmetric Square
LU Decomposition | lu(X, [L_only, U_only, overwrite]) | X = L @ U | Any Matrix
Singular Value Decomposition | svd(X, [U_decision, overwrite]) | X = U * S @ V.T | Any Matrix
QR Decomposition | qr(X, [Q_only, R_only, overwrite]) | X = Q @ R | Any Matrix

## Eigenvalue Problems

Symmetric EigenDecomposition | eigh(X, [alpha, svd, overwrite]) | X = V * L @ V^-1 | Symmetric Square

## Matrix Inversion

Cholesky Inverse | cho_inv(X, [turbo]) | inv(X) @ X = I | Symmetric Square
Pseudoinverse (Cholesky) | pinvc(X, [alpha, turbo]) | inv(X) @ X = I | Any Matrix
Symmetric Pseudoinverse | pinvh(X, [alpha, turbo, n_jobs]) | inv(X) @ X = I | Symmetric Square
Pseudoinverse (SVD) | pinv(X, [alpha, overwrite]) | inv(X) @ X = I | Any Matrix
Pseudoinverse (LU Decomp) | pinvl(X, [alpha, turbo, overwrite]) | inv(X) @ X = I | Square Matrix