Generalized inverses of cone preserving maps

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Title:	Generalized inverses of cone preserving maps
Authors:	Tam, Bit-shun
Contributors:	淡江大學數學學系
Date:	1981-10
Issue Date:	2010-01-28 07:28:56 (UTC+8)
Publisher:	New York : Elsevier Inc.
Abstract:	Let K1 and K2 be solid cones in Rn and Rm respectively, and let A be a linear operator such that AK1⊆K2. Necessary and sufficient conditions for the existence of various kinds of generalized inverses of A taking K2 into K1 are given. Projections which belong to π(K), the set of all linear operators that preserve a are studied. In particular, it is proved that a projection P in π(K) is a simplicial nonnegative linear combination of its rank-one operators iff Im P∩K is a simplical cone. An open question of Burns, Fiedler, and Haynsworth concerning minimal generating matrices of polyhedral cones is also extended and answered affirmatively.
Relation:	Linear Algebra and Its Applications 40, pp.189-202
DOI:	10.1016/0024-3795(81)90149-X
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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