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 ^[1]

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

See also

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

References

1. Young, David M. (1971). Iterative solution of large linear systems . Computer Science and Applied Mathematics. Academic Press. ISBN   0127730508. LCCN   73-170124.