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Miranda and Thompson's trace inequality and a log convexity result

✍ Scribed by Tin-Yau Tam

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
873 KB
Volume
262
Category
Article
ISSN
0024-3795

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✦ Synopsis

A geometric proof of Miranda and Thompson's trace inequality is given, via Thompson's singular-value-diagonal-element inequalities. Miranda and Thompson's trace inequality is associated with the unitary group. We then deal with the cases associated with the orthogonal group and the special unitary group. We also discuss the convexity of the set of the diagonal elements of complex matrices with fixed singular values and determinant. Some question are asked. A log convexity result related to Gram-Schmidt decomposition is obtained.

πŸ“œ SIMILAR VOLUMES

On the dual of a result of Miranda and T
On the dual of a result of Miranda and Thompson
✍ NatΓ‘lia Bebiano; J. da ProvidΓͺncia πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 475 KB

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

On Lei, Miranda, and Thompson's result o
On Lei, Miranda, and Thompson's result on singular values and diagonal elements
✍ Tin-Yau Tam πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 599 KB

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