Generalized inverses of matrices over a finite field

✍ Scribed by John D. Fulton

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 657 KB
• Volume: 21
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(78)90144-9

✦ Synopsis

For a given m X n matrix A of rank I ov+r a finite field F, the number of generalized invers:s, of reflexive generalized inverses, of normalized generalized inverses, and of pseudoinverses of A are derermined by elementary methods. The more dticult problem of determining which m X n matrices A of rank I over F have normalized genevbed inverses and which hatye pseudoinverses is soived. Moreover, the number of such matrices v*hich possess normelkd generalized inverses and the number which possess pseudoinverses are fotind.