×

Drazin inverses and canonical forms in \(M_ 0(\)Z/h). (English) Zbl 0455.15003


MSC:

15A09 Theory of matrix inversion and generalized inverses
15A21 Canonical forms, reductions, classification
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ben Israel, A.; Greville, T. N.E., Generalized Inverses, Theory and Applications (1974), Wiley: Wiley New York · Zbl 0305.15001
[2] Campbell, S. L.; Meyer, C. D., Generalized Inverses of Linear Transformations (1979), Pitman: Pitman New York · Zbl 0417.15002
[3] Drazin, M. P., Pseudo-inverses in Associated Rings and Semigroups, Amer. Math. Monthly, 65, 506-514 (1958) · Zbl 0083.02901
[4] Donovan, T. P., Certain Matrix Congruences mod \(p^n\), Ann. Mat. Pura Appl. IV, 65, 193-214 (1977) · Zbl 0374.15005
[5] Fuller, L. E., A canonical set of matrices over a principal ideal ring modulo \(m\), Canad. J. Math., 7, 54-58 (1955) · Zbl 0064.01603
[6] Gantmacher, F. R., The Theory of Matrices, Vol. 1 (1960), Chelsea, New York · Zbl 0088.25103
[7] Hartwig, R. E., A note on periodic matrices, J. Industrial Soc., 27, 51-55 (1977), part 1 · Zbl 0391.15004
[10] Hartwig, R. E.; Shoaf, J., Group inverses and Drazin inverses of bidiagonal and triangular Toeplitz matrices, J. Austral. Math. Soc. Ser. A, 24, 10-34 (1977) · Zbl 0372.15003
[11] Kaplansky, I., Fields and Rings (1965), Univ. of Chicago Press: Univ. of Chicago Press Chicago
[12] Levine, J.; Hartwig, R. E., Applications of the Drazin inverse to the Hill cryptographic system, I, Cryptologia, 4, 71-83 (1980) · Zbl 0427.94015
[13] McCoy, N. H., Rings and Ideals, Carus Monograph No. 8 (1948), Buffalo · Zbl 0079.26303
[14] McDonald, B. R., Finite Rings with Identity (1974), M. Dekker: M. Dekker New York · Zbl 0294.16012
[15] Roth, W. E., The equations \(AX − YB =C\) and \(AX − XB =C\) in Matrices, Proc. Amer. Math. Soc., 3, 392-396 (1952) · Zbl 0047.01901
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.