Minimizing the Cayley transform of an orthogonal matrix by multiplying by signature matrices

被引：2

作者：

O'Dorney, Evan ^{[1
]}

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 448卷

关键词：

Cayley transform; Signature matrix; Principal minor;

D O I：

10.1016/j.laa.2014.01.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Cayley transform, $(A) = (I - A) (I + A)(-1), maps skew-symmetric matrices to orthogonal matrices and vice versa. Given an orthogonal matrix Q, we can choose a diagonal matrix D with each diagonal entry +/- 1 (a signature matrix) and, if I + QD is nonsingular, calculate the skew-symmetric matrix $(QD). An open problem is to show that, by a suitable choice of D, we can make every entry of $(QD) less than or equal to 1 in absolute value. We solve this problem by showing that the principal minors of $(QD) are related in a simple way to the principal minors of $(Q). (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：97 / 103

页数：7