nLab
matrix equivalence

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

Equality and Equivalence

Contents

Definition

Two matrices A,BMat n×m(R)A,B \in Mat_{n \times m}(R) are called matrix equivalent if there exist invertible matrices PGL(n,R)P \in GL(n,R), QGL(m,R)Q \in GL(m,R) such that A 2A_2 equals the matrix product

A 2=PA 1Q. A_2 \;=\; P \cdot A_1 \cdot Q \,.

References

See also

Created on September 19, 2018 at 05:10:30. See the history of this page for a list of all contributions to it.