A square matrix is called a -matrix if all off-diagonal entries are less than or equal to zero.

Z-matrix arises naturally in solving Dirichlet problem numerically, and linear modeling of economy.

Reference:

M. Fiedler, Special matrices and their applications in numerical mathematics, 1986, Martinus Nijhoff Publishers, Dordrecht.

R. A. Horn and C. R. Johnson, Topics in matrix analysis, 1991, Cambridge University Press, United Kingdom.

R. B. Bapat and T. E. S. Raghavan, Nonnegative matrices and applications, 1997, Cambridge University Press, United Kingdom.