Vector Majorization Via Hessenberg Matrices |
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Authors: | Brualdi Richard A; Hwang Suk-Geun |
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Institution: | Department of Mathematics, University of Wisconsin Madison, WI 53706, USA
Department of Mathematics Education, Kyungpook University Taegu 702-701, Republic of Korea |
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Abstract: | In this paper it is proved that, for real n-vectors x and y,x is majorized by y if and only if x = PHQy for some permutationmatrices P, Q, and for some doubly stochastic matrix H whichis a direct sum of doubly stochastic Hessenberg matrices. Thisresult reveals that any n-vector which is majorized by a vectory can be expressed as a convex combination of at most (n2 –n + 2)/2 permutations of y. |
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