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Linear operators preserving the minimal rank

โœ Scribed by Wasin So


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
66 KB
Volume
302-303
Category
Article
ISSN
0024-3795

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โœฆ Synopsis


The minimal rank of a square matrix is studied, and the linear operators preserving it are characterized. Some related results are presented and some unsolved problems are discussed.


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Let F be an arbitrary field and k 2 be an arbitrary fixed integer. A k-tuple of matrices for all ฯƒ โˆˆ S k , where S k is a symmetric group on k elements. We investigate the set of linear operators on M n (F) that preserve the set of rank permutable matrix k-tuples.