Linear and multilinear algebra; matrix theory Nonnegative and stochastic matrices Concept
Irreducible matrix
Summary
A square matrix is irreducible when no simultaneous permutation of its rows and columns puts it into block upper triangular form. For a nonnegative matrix this means that its directed graph is strongly connected: every index can reach every other index. Irreducibility is the main hypothesis of the Perron–Frobenius theorem for nonnegative matrices that are not positive.
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| Tag | 7Q60BB01YG |
|---|---|
| URI | m2://7Q60BB01YG |
| Kind | concept |
| Writing | W0 stub |
| MSC | 15B48, 05C50 |
| Specializes | Square matrix |
| Changed | 2 November 2026 |
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