Nonnegative matrix: Difference between revisions

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

In [[mathematics]], a '''nonnegative matrix''', written
: <math>\mathbf{X} \geq 0,</math>
is a [[matrix (mathematics)|matrix]] in which all the elements are equal to or greater than zero, that is,

: <math>\mathbfx_{Xij} \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 commonly found, the term is only occasionally used due to the possible confusion with [[positive-definite matrix|positive-definite matrices]], which are different.