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In mathematics, the class of L-matrices are those matrices whose off-diagonal entries are less than or equal to zero and whose diagonal entries are positive; that is, an L-matrix L satisfies[1]

$${\displaystyle L=(\ell _{ij});\quad \ell _{ii}>0;\quad \ell _{ij}\leq 0,\quad i\neq j.}$$

Z-matrix
Metzler matrix

References

Young, David M. (1971). "Iterative solution of large linear systems". Academic Press, New York-London.