View source for 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 [[matrix (mathematics)|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<ref name="Young1971">{{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}}</ref>

:<math>L=(\ell_{ij});\quad \ell_{ii} > 0; \quad \ell_{ij}\leq 0, \quad i\neq j.</math>

==See also==
* [[Z-matrix_(mathematics)|Z-matrix]]—every L-matrix is a Z-matrix
* [[Metzler matrix]]—the negation of any L-matrix is a Metzler matrix

==References==
{{reflist}}

[[Category:Matrices]]


{{matrix-stub}}