Matrix Trace Inequalities Involving Simple, Kronecker, and Hadamard Product

Heinz Neudecker, Shuangzhe LIU

Research output: Contribution to journalArticle

Abstract

Solution, proposed by Heinz Neudecker and Shuangzhe Liu. Let Xg(N) be the largest eigenvalue of N. We use the relationships (a) tr(A 0 B) = trAtrB, and (b) N (Q) L = Jp (N 0 L)Jp, where N and L are p x p matrices, and the selection matrix Jp with property JpJp = Ip, as defined in Amemiya (1985), Kollo and Neudecker (1993), and Neudecker (1993).
Original languageEnglish
Pages (from-to)669-670
Number of pages2
JournalEconometric Theory
Volume11
Issue number3
DOIs
Publication statusPublished - 1 Jan 1995
Externally publishedYes

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abstract = "Solution, proposed by Heinz Neudecker and Shuangzhe Liu. Let Xg(N) be the largest eigenvalue of N. We use the relationships (a) tr(A 0 B) = trAtrB, and (b) N (Q) L = Jp (N 0 L)Jp, where N and L are p x p matrices, and the selection matrix Jp with property JpJp = Ip, as defined in Amemiya (1985), Kollo and Neudecker (1993), and Neudecker (1993).",
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Matrix Trace Inequalities Involving Simple, Kronecker, and Hadamard Product. / Neudecker, Heinz; LIU, Shuangzhe.

In: Econometric Theory, Vol. 11, No. 3, 01.01.1995, p. 669-670.

Research output: Contribution to journalArticle

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N2 - Solution, proposed by Heinz Neudecker and Shuangzhe Liu. Let Xg(N) be the largest eigenvalue of N. We use the relationships (a) tr(A 0 B) = trAtrB, and (b) N (Q) L = Jp (N 0 L)Jp, where N and L are p x p matrices, and the selection matrix Jp with property JpJp = Ip, as defined in Amemiya (1985), Kollo and Neudecker (1993), and Neudecker (1993).

AB - Solution, proposed by Heinz Neudecker and Shuangzhe Liu. Let Xg(N) be the largest eigenvalue of N. We use the relationships (a) tr(A 0 B) = trAtrB, and (b) N (Q) L = Jp (N 0 L)Jp, where N and L are p x p matrices, and the selection matrix Jp with property JpJp = Ip, as defined in Amemiya (1985), Kollo and Neudecker (1993), and Neudecker (1993).

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M3 - Article

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