nLab inverse matrix

Properties

Proposition

(fundamental theorem of invertible matrices)

For $n \in \mathbb{N}$ and $A \in Mat_{n \times n}(k)$ a square matrix, the following are equivalent:

1. $A$ is an invertible matrix;

2. $A$ is the matrix product of elementary matrices?.

Related concepts

• matrix group

• general linear group

• matrix equivalence

References

• Wikipedia, Invertible matrix

• WolframMathWorld, Invertible Matrix Theorem