M-matrix products having positive principal minors
- 1 December 1984
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 16 (1-4) , 29-38
- https://doi.org/10.1080/03081088408817607
Abstract
Sufficient conditions are given for powers and products of M-matrices to have all principal minors positive. Several of these conditions involve directed graphs of the matrices. In particular we show that if A and B are irreducible M-matrices which have longest simple circuit of length two with A+B having no simple circuit longer than three, then the product AB has all principal minors positive.Keywords
This publication has 6 references indexed in Scilit:
- A Class of M-Matrices with Tree GraphsSIAM Journal on Algebraic Discrete Methods, 1983
- Totally Nonnegative,M-, and Jacobi MatricesSIAM Journal on Algebraic Discrete Methods, 1980
- Combinatorially symmetric matricesLinear Algebra and its Applications, 1974
- A class of positive stable matricesJournal of Research of the National Bureau of Standards, Section B: Mathematical Sciences, 1974
- Matrices of class J2Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, 1967
- The symmetrization of matrices by diagonal matricesJournal of Mathematical Analysis and Applications, 1962