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Article
Matrix Inequalities by Means of Embedding
Electronic Journal of Linear Algebra
  • Tian-Gang Lei, National Natural Science Foundation of China
  • Ching-Wah Woo, University of Hong Kong
  • Fuzhen Zhang, Nova Southeastern University; Shenyang Normal University
Document Type
Article
Publication Date
4-1-2004
Keywords
  • Eigenvalue,
  • Majorization,
  • Matrix absolute value,
  • Matrix inequality,
  • Matrix norm,
  • Normal matrix,
  • Positive semidefinite matrix,
  • Singular value,
  • Spread,
  • Wielandt inequality
Disciplines
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
Citation Information
Tian-Gang Lei, Ching-Wah Woo and Fuzhen Zhang. "Matrix Inequalities by Means of Embedding" Electronic Journal of Linear Algebra Vol. 11 (2004) p. 66 - 67 ISSN: 1081-3810
Available at: http://works.bepress.com/fuzhen-zhang/82/