A nonnegative matrix is a real or integer matrix (a)_(i j) for which each matrix element is a nonnegative number, i.e., a_(i j)>=0 for all i, j. Nonnegative matrices are therefore a superset of positive matrices. Nonnegative matrices are important in a variety of applications and have a number of attractive mathematical properties. Together with positive semidefinite matrices, they therefore serve as a natural generalization of nonnegative real numbers. The most fundamental properties of nonnegative matrices require fairly advanced mathematics and were established by Perron and Frobenius.

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