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On Lei, Miranda, and Thompson's result on singular values and diagonal elements

✍ 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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✦ 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.


πŸ“œ SIMILAR VOLUMES


Singular values, diagonal elements, and
✍ Hector F. Miranda πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 75 KB

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.

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