Basic Properties of the Poverse of a Matrix.
TEXAS UNIV AT AUSTIN CENTER FOR CYBERNETIC STUDIES
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Some basic properties of poverses of matrices are studied. Previous characterizations are extended and a new one is given in terms of a super eigenvector which may be useful in non-linear inequalities theory. It is shown that the existence of poverses is independent of the rank of the matrices involved and that there are poverses of every rank. The convex set of poverses is characterized for a given matrix in terms of systems of linear inequalities which are amenable to linear programming computation. Some characterizations are also given of the extreme points of related non-polyhedral convex sets. Finally, some conditions connected with the actual computation of poverses are investigated.
- Theoretical Mathematics