It is shown that if A is an integral matrix having linearly independent rows, then the extreme points of the set of nonnegative solutions to Ax = b are integral for all integral b if and only if the determinant of every basis matrix is plus or minus 1. This provides a short proof of the Hoffman-Kruskal theorem characterizing unimodular matrices, i.e., matrices in which the determinant of each nonsingular submatrix is plus or minus 1. Their theorem is that if A is integral, then A is unimodular if and only if the extreme points of the set of nonnegative solutions to Ax = or <b are integral for all integral b. (Author).
"It is shown that if A is an integral matrix having linearly independent rows, then the extreme points of the set of nonnegative solutions to Ax = b are integral for all integral b if and only if the determinant of every basis matrix is plus or minus 1. This provides a short proof of the Hoffman-Kruskal theorem characterizing unimodular matrices, i.e., matrices in which the determinant of each nonsingular submatrix is plus or minus 1. Their theorem is that if A is integral, then A is unimodular if and only if the extreme points of the set of nonnegative solutions to Ax = or <b are integral for all integral b. (Author)."@en
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This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.