# DAVIDSTUTZ

## PHP Matrix Decompositions

This library implements common matrix decompositions in PHP. An interactive demo application provides the theoretical background and can be used to compute these matrix decompositions. The following table provides an overview:

Decomposition Factorization Applicable for Runtime
LU $A = LU$ $A \in \mathbb{R}^{n \times n}$, $A$ regular $\mathcal{O}(\frac{1}{3}n^3)$
Cholesky $A = LDL^T$ $A \in \mathbb{R}^{n \times n}$, $A$ symmetric and positive definite $\mathcal{O}(\frac{1}{6}n^3)$
QR: Givens Rotations $A = QR$ $A \in \mathbb{R}^{m \times n}$ $\mathcal{O}(\frac{4}{3}n^3)$
QR: Householder Transformations $A = QR$ $A \in \mathbb{R}^{m \times n}$ $\mathcal{O}(\frac{2}{3}n^3)$

The demonstration application is available on GitHub as well, however, as separate repository.