Journal article
Semipositive matrices and their semipositive cones
Positivity : an international journal devoted to the theory and applications of positivity in analysis, Vol.22(1), pp.379-398
03/2018
Handle:
https://hdl.handle.net/2376/113231
Abstract
The semipositive cone of $$A\in \mathbb {R}^{m\times n}, K_A = \{x\ge 0\,:\, Ax\ge 0\}$$
A∈Rm×n,KA={x≥0:Ax≥0}
, is considered mainly under the assumption that for some $$x\in K_A, Ax>0$$
x∈KA,Ax>0
, namely, that A is a semipositive matrix. The duality of $$K_A$$
KA
is studied and it is shown that $$K_A$$
KA
is a proper polyhedral cone. The relation among semipositivity cones of two matrices is examined via generalized inverse positivity. Perturbations and intervals of semipositive matrices are discussed. Connections with certain matrix classes pertinent to linear complementarity theory are also studied.
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Details
- Title
- Semipositive matrices and their semipositive cones
- Creators
- K Sivakumar - 0000 0001 2315 1926 grid.417969.4 Department of Mathematics Indian Institute of Technology Madras Chennai 600 036 IndiaM Tsatsomeros - 0000 0001 2157 6568 grid.30064.31 Department of Mathematics and Statistics Washington State University Pullman WA 99164 USA
- Publication Details
- Positivity : an international journal devoted to the theory and applications of positivity in analysis, Vol.22(1), pp.379-398
- Academic Unit
- Mathematics and Statistics, Department of
- Publisher
- Springer International Publishing; Cham
- Identifiers
- 99900548106501842
- Language
- English
- Resource Type
- Journal article