Matrix Trace Inequalities Involving Simple, Kronecker, and Hadamard Product

Heinz Neudecker; Shuangzhe LIU

doi:10.1017/S026646660000966X

Matrix Trace Inequalities Involving Simple, Kronecker, and Hadamard Product

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	669-670
Number of pages	2
Journal	Econometric Theory
Volume	11
Issue number	3
DOIs	https://doi.org/10.1017/S026646660000966X
Publication status	Published - 1 Jan 1995
Externally published	Yes

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title = "Matrix Trace Inequalities Involving Simple, Kronecker, and Hadamard Product",

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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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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