Generalized inverses of matrices over a finite field |
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Authors: | John D Fulton |
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Institution: | Clemson University, Dept of Mathematical Sciences, College of Sciences, Clemson, SC 29631, U.S.A. |
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Abstract: | For a given m × n matrix A of rank r over a finite field F, the number of generalized inverses, of reflexive generalized inverses, of normalized generalized inverses, and of pseudoinverses of A are determined by elementary methods. The more difficult problem of determining which m × n matrices A of rank r over F have normalized generalized inverses and which have pseudoinverses is solved. Moreover, the number of such matrices which possess normalized generalized inverses and the number which possess pseudoinverses are found. |
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