Quasipositive matrix

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In mathematics, especially linear algebra, a matrix is called quasipositive if all of its elements are non-negative except for those on the main diagonal, which are unconstrained. That is, a quasipositive matrix is any matrix A which satisfies

A=(a_{ij});\quad a_{ij}\geq 0, \quad i\neq j.

Quasipositive matrices are also sometimes referred to as Z( − )-matrices, as a Z-matrix is equivalent to a negated quasipositive matrix.

The exponential of a quasipositive matrix is a nonnegative matrix.

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