R. Checa-Garcia webpage | Linear Algebra

Notebook

### Linear Algebra and Computing

Scientific Computing and Linear Algebra

COMPUTING-BLOG

### Introduction

This post just remember several linear algebra properties that are relevant for scientific programming.

### Reducible Matrix

Definition: An square matrix A is reducible if there is a matrix P (basis change) such that,

This property is very useful because the typical linear system solution $Ay=c$ is now more easy to resolve in terms of computing because

The subsystem $B_{22}y_{2}=c_{2}$ is indepentent of the other B matrices with the logical computational improvement.