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 14:46:20. See the history of this page for a list of all contributions to it.