L-matrix

{{Short description|Matrix with positive entries on the main diagonal and non-positive entries elsewhere}}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{{cite book|last1=Young|first1=David M.|title=Iterative solution of large linear systems|url=https://archive.org/details/iterativesolutio00youn|url-access=registration|publisher=Academic Press|year=1971 |series=Computer Science and Applied Mathematics |lccn=73-170124 |isbn=0127730508}}

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