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.
| Original language | English |
|---|---|
| Pages (from-to) | 66-77 |
| Journal | Electronic Journal of Linear Algebra |
| Volume | 11 |
| Online published | 1 Jan 2004 |
| DOIs | |
| Publication status | Published - Apr 2004 |
Research Keywords
- Eigenvalue
- Majorization
- Matrix absolute value
- Matrix inequality
- Matrix norm
- Normal matrix
- Positive semidefinite matrix
- Singular value
- Spread
- Wielandt inequality
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