L-matrix

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

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

• Z-matrix—every L-matrix is a Z-matrix
• Metzler matrix—the negation of any L-matrix is a Metzler matrix