Abstract
Semimonotone matrices A are those real matrices for which the operation Ax does not negate all positive entries of any nonzero, entrywise nonnegative vector x. In that respect, semimonotone matrices generalize the class of matrices all of whose principal minors are nonnegative. As such, they play an important role in the solution of the linear complementarity problem. Properties of semimonotone matrices that are largely analogous to the properties of the matrix classes they generalize are reviewed and developed.
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