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Group inverses and Drazin inverses of bidiagonal and triangular Toeqlitz matrices
Published online by Cambridge University Press: 09 April 2009
Abstract
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Necessary and sufficient sonditions are given for the existence of the group and Drazin inverses of bidiagonal and triangular Toeplitz matrices over an arbitrary ring.
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- Copyright © Australian Mathematical Society 1977
References
Ben-Israel, A. and Greville, T. N. (1974), Generalised Inverses Theory and Applications (Wiley, New York).Google Scholar
Cline, Randall E. (1965), ‘An application of representations for the generalised inverse of a matrix’ (MRC Technical Report, 592).Google Scholar
Cullen, Charles G. (1972), Matrices and Linear Transformations, Second Edition (Addison-Wesley, Reading, Massachusetts; Menlo Park, California; London; Don Mills, Ontario).Google Scholar
Drazin, M. P. (1958), ‘Pseudo-inverses in associated rings and semigroups’, Amer. Math. Monthly 65, 506–514.CrossRefGoogle Scholar
Gantmacher, F. R. (1960). The Theory of Matrices, Volume One (translated by Hirsch, K. A.; Chelsea, New York).Google Scholar
Hartwig, R. E. (1974). ‘Some properties of hypercompanion matrices’. Industrial Math. 24, Part 2. 77–84.Google Scholar
Hartwig, R. E. (1975). ‘AX − XB = C, resultants and generalized inverses’, SIAM J. Appl. Math. 28, 154–183.CrossRefGoogle Scholar
Hartwig, R. E. (1976). ‘Block generalised inverses’. Arch. Rational Mech. Anal. 61, # 3, 197–251.CrossRefGoogle Scholar
Hartwig, R. E. (to appear). ‘Generalised inverses, EP elements and associates’. Rev. Roumaine Math. Pures Appl.Google Scholar
Henriksen, Melvin (1973), ‘On a class of regular rings that are elementary divisor rings’, Arch. Math. (Basel) 24, 133–141.CrossRefGoogle Scholar
Huang, Nancy M. and Cline, Randall E. (1972), ‘Inversion of persymmetric matrices having Toeplitz inverses’, J. Assoc. Comput. Mach. 19, 437–444.CrossRefGoogle Scholar
Jacobson, Nathan (1943), The Theory of Rings (Mathematical Surveys, II. Amer. Math. Soc., New York City).CrossRefGoogle Scholar
Jacobson, Nathan (1953), Lectures in Abstract Algebra. Volume II. Linear Algebra (Van Nostrand, Princeton, New Jersey; Toronto; New York; London).Google Scholar
Meyer, C. D. (1975), ‘The role of the group generalized inverse in the theory of finite Markov chains’, SIAM. Rev. 17, 443–464.CrossRefGoogle Scholar
Meyer, C. D. and Rose, N. J. (submitted), ‘The index and the Drazin inverse of block triangular matrices’.Google Scholar
Roth, William E. (1952), ‘The equations AX − YB = C and AX − XB = C in matrices’, Proc. Amer. Math. Soc. 3, 392–396.Google Scholar
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