Nonnegative matrix: Difference between revisions

Revision as of 11:37, 27 September 2014

Revision as of 22:04, 27 September 2014

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{{Original research|article|date=September 2014}}

{{hatnote|Not to be confused with [[Totally positive matrix]] and [[Positive-definite matrix]].}}

In [[mathematics]], a '''nonnegative matrix''' is a [[matrix (mathematics)|matrix]] in which all the elements are equal to or greater than zero

: <math>\mathbf{X} \geq 0, \qquad \forall {i,j}\quad x_{ij} \geq 0.</math>

A '''positive matrix''' is a matrix in which all the elements are greater than zero. The set of positive matrices is a subset of all non-negative matrices. While such matrices are very common, especially the [[transition matrix]] for a [[Markov chain]], the term is only occasionally used due to the possible confusion with [[positive-definite matrix|positive-definite matrices]], which are different.

Any [[transition matrix]] for a [[Markov chain]] is a non-negative matrix.

A rectangular non-negative matrix can be approximated by a decomposition with two other non-negative matrices via [[non-negative matrix factorization]].