Minimum upper bound of the Cayley transform of an orthogonal matrix multiplied by signed permutation matrices

被引：0

作者：

Mitamura, Takuma ^{[1
]}

Tanaka, Akira ^{[2
]}

机构：

[1] Res Inst Syst Planning Inc, Nihonkaikan, 18-6 Sakuragaoka, Shibuya, Tokyo 1500031, Japan

[2] Hokkaido Univ, Fac Informat Sci & Technol, N14W9, Kita Ku, Sapporo, Hokkaido 0600814, Japan

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 659卷

关键词：

Skew-symmetric matrix; Cayley transform; Orthogonal matrix; Signed permutation matrix;

D O I：

10.1016/j.laa.2022.11.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

O'Dorney has proved that for any orthogonal matrix U, there exists a signature matrix D (a diagonal matrix with diagonal entries & PLUSMN;1) by which |sij| & LE; 1, where S = (sij) = Q(UD) the upper bound can be reduced to & RADIC;2 - 1 by multiplying by is the Cayley transform of UD. In this paper, we prove that a certain signed permutation matrix, instead of a signature matrix. & COPY; 2022 Elsevier Inc. All rights reserved.

引用

页码：24 / 32

页数：9

共 4 条

[1] Minimizing the Cayley transform of an orthogonal matrix by multiplying by signature matrices
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[2] Special paraunitary matrices, Cayley transform, and multidimensional orthogonal filter banks
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[3] NATURAL GRADIENT APPROACH IN ORTHOGONAL MATRIX OPTIMIZATION USING CAYLEY TRANSFORM
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[4] The decomposition of an arbitrary 2w x 2w unitary matrix into signed permutation matrices
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