Nonnegative matrix: Difference between revisions

Revision as of 23:59, 18 July 2020

Revision as of 02:42, 22 January 2021

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The inverse of any [[Invertible matrix|non-singular]] [[M-matrix]] {{Clarify|reason=relation to subject of nonnegative matrix not made clear; what is an M-matrix?|date=March 2015}} is a non-negative matrix. If the non-singular M-matrix is also symmetric then it is called a [[Stieltjes matrix]].

The inverse of a non-negative matrix is usually not non-negative. The exception is the non-negative [[monomial matrices]]: a non-negative matrix has non-negative inverse if and only if it is a (non-negative) monomial matrix. Note that thus the inverse of a positive matrix is not positive or even non-negative, as positive matrices are not monomial, for dimension <{{math>|''n'' > 1}}.</math>

== Specializations ==