On the distinguished eigenvalues of a cone-preserving map

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Journal Article > Item 987654321/41378

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Title:	On the distinguished eigenvalues of a cone-preserving map
Authors:	Tam, Bit-Shun
Contributors:	淡江大學數學學系
Date:	1990-04
Issue Date:	2013-06-13 11:25:26 (UTC+8)
Publisher:	Philadelphia: Elsevier Inc.
Abstract:	We generalize many known results on a nonnegative matrix concerning linear inequalities, Collatz-Wielandt sets, and generalized eigenvectors to the setting of a matrix preserving a (finite-dimensional) proper cone. A simple cone-theoretic proof is given for the nonnegative-basis theorem for the algebraic eigenspace of a nonnegative matrix. The result is also extended to a matrix preserving a polyhedral cone. Given proper cones K1 and K2 in different euclidean spaces, a necessary and sufficient condition is also obtained for the existence of a nonzero matrix X which takes K2 into K1 and satisfies AX = XB, where A, B are given matrices preserving K1 and K2 respectively. This extends and answers a recent open question posed by Hartwig.
Relation:	Linear Algebra and Its Applications 131(C), pp.17-37
DOI:	10.1016/0024-3795(90)90372-J
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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