In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a Q-matrix is a square
matrix
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** '' The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...
whose associated
linear complementarity problem LCP(''M'',''q'') has a solution for every vector ''q''.
Properties
* ''M'' is a Q-matrix if there exists ''d'' > 0 such that LCP(''M'',0) and LCP(''M'',''d'') have a unique solution.
* Any
P-matrix is a Q-matrix. Conversely, if a matrix is a
Z-matrix and a Q-matrix, then it is also a P-matrix.
See also
*
P-matrix
*
Z-matrix
References
*
*
*
*
Matrix theory
Matrices
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