Irreducible matrices †
- 1 January 1974
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 1 (4) , 337-342
- https://doi.org/10.1080/03081087408817033
Abstract
Frobenius proved that if Ais an irreducible matrix, then there exists a permutation matrix Psuch that PAPT is equal to a partitioned matrix (Aij)whose main diagonal blocks A11 ,…Ann are square and all its blocks except A12A23,…Ah-1,hAh1 are zero. It is shown that a nonnegative matrix in this form is irreducible with index of imprimitivity hif and only if it has no zero rows nor columns and the product A12A23… Ah1 is primitive. It is also shown that if Ais nonsingular, then each of the blocks A12, A23,…, Ah1 is n/h-square.Keywords
This publication has 1 reference indexed in Scilit:
- XXXIX. On the equation to the secular inequalities in the planetary theoryJournal of Computers in Education, 1883