# General Linear System (Linear System)

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## Description

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables. This is typically written in the form $Ax=b$ where $A$ is a matrix and $x, b$ are vectors. In this case, we impose no restrictions on $A$.

## Related Problems

Subproblem: Sparse Linear System, Positive Definite, Hermitian Matrix, Non-Definite, Symmetric Matrix, Toeplitz Matrix, Vandermonde Matrix

Related: Positive Definite, Hermitian Matrix, Non-Definite, Symmetric Matrix, Toeplitz Matrix, Vandermonde Matrix

## Parameters

$n$: number of variables and number of equations

$m$: number of nonzero entries in matrix

$k$: ratio between largest and smallest eigenvalues

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Gaussian-Jordan Elimination | -150 | $O(n^{3})$ | $O(n^{2})$ | Exact | Deterministic |