Mathematics Faculty Articles

Title

Matrix Inequalities by Means of Embedding

Document Type

Article

Publication Date

4-1-2004

Publication Title

Electronic Journal of Linear Algebra

Keywords

Eigenvalue, Majorization, Matrix absolute value, Matrix inequality, Matrix norm, Normal matrix, Positive semidefinite matrix, Singular value, Spread, Wielandt inequality

ISSN

1081-3810

Volume

11

First Page

66

Last Page

67

Abstract

In this expository study some basic matrix inequalities obtained by embedding bilinear forms 〈Ax, x〉 and 〈Ax, y〉 into 2 × 2 matrices are investigated. Many classical inequalities are reproved or refined by the proposed unified approach. Some inequalities involving the matrix absolute value |A| are given. A new proof of Ky Fan’s singular value majorization theorem is presented.

Comments

AMS subject classifications. 15A42, 15A63, 47B15

DOI

10.13001/1081-3810.1123