On the singular value decomposition over finite fields and orbits of GU X GU

• Published in: Indagationes mathematicae Vol. 32; no. 5; p. 1083
• Main Author: Guralnick, Robert M
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Science Ltd 01.09.2021
• Subjects: Decomposition; Fields (mathematics); Group theory; Linear algebra; Mathematical analysis; Matrix algebra; Motivation; Orbits; Singular value decomposition
• ISSN: 0019-3577; 1872-6100
• DOI: 10.1016/j.indag.2021.01.006

The singular value decomposition of a complex matrix is a fundamental concept in linear algebra and has proved extremely useful in many subjects. It is less clear what the situation is over a finite field. In this paper, we classify the orbits of GUm(q)×GUn(q) on Mm×n(q2) (which is the analog of the...