For complex matrices A and B there are inequalities related to the diagonal elements of AB and the singular values of A and B. We study the conditions on the matrices for which those inequalities become equalities. In all cases, the conditions are both necessary and sufficient.
On Lei, Miranda, and Thompson's result on singular values and diagonal elements
β Scribed by Tin-Yau Tam
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 599 KB
- Volume
- 272
- Category
- Article
- ISSN
- 0024-3795
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β¦ Synopsis
Thomspon and Sing's result on the singular values and the diagonal elements of a complex n X n matrix has been recently extended to arbitrary m matrices, by Lei and by Miranda and Thompson independently. The real case in which the determinant of the product of the m real matrices is nonnegative (or nonpositive) was raised by Miranda and Thompson.
In this note, we provide an answer to the question, and we also extend some other results of Lei.
π SIMILAR VOLUMES
For A and B real matrices with prescribed singular values, Miranda and Thompson characterized maxtr(AUBV) when U and V range over SO(n), the real proper orthogonal group. Motivated by this result, we investigate the location of deft A + UBV) for A, B, U, V as previously. The corresponding problem fo
Using the notion of weighted sharing of values we prove two uniqueness theorems which improve the results proved by T.C. Alzahary [T.C. Alzahary, Weighted sharing three values and Brosch's theorem.