#
nLab
Gaussian elimination

Contents
### Context

#### Linear algebra

**homotopy theory, (∞,1)-category theory, homotopy type theory**

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…

models: topological, simplicial, localic, …

see also **algebraic topology**

**Introductions**

**Definitions**

**Paths and cylinders**

**Homotopy groups**

**Basic facts**

**Theorems**

# Contents

## Idea

What is called *Gaussian elimination* is an algorithm for solving systems of linear equations. It proceeds by encoding the system as a suitable matrix and then applying elementary row operations to bring it into upper triangular form.

## In constructive mathematics

Gaussian elimination only works for discrete fields such as the rational numbers or the algebraic numbers. The algorithm does not work for other types of fields such as Heyting fields, which means that it doesn’t work for the real numbers, however defined.

## References

Last revised on May 11, 2022 at 18:46:20.
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