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A determinant for rectangular matrices

  • V.N. Joshi (a1)
Abstract

The familiar notion of the determinant is generalised to include rectangular matrices. An expression for a normalised generalised inverse of a matrix is given in terms of its determinant and a possible generalisation of the Schur complement is discussed as a simple application.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1980
References
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[1]Goldman, A.J. and Zelan, M., “Weak generalized inverses and minimum variance linear unbiased estimation”, J. Res. Nat. Bur. Standards Sect. B 68 (1964), 151–172.
[2]Haynsworth, Emilie V., “Applications of an inequality for the Schur complement”, Proc. Amer. Math. Soc. 24 (1970), 512–516.
[3]Householder, Alston S., The theory of matrices in numerical analysis (Blaisdell [Ginn and Company], New York, Toronto, London, 1964).
[4]Jurkat, W.B. and Ryser, H.J., “Matrix factorizations of determinants and permanents”, J. Algebra 3 (1966), 1–27.
[5]Morris, Gerald L. and Odell, Patrick L., “A characterization for generalized inverses of matrices”, SIAM Rev. 10 (1968), 208–211.
[6]Penrose, R., “A generalized inverse for matrices”, Proc. Cambridge Philos. Soc. 51(1955), 406–413.
[7]Searle, S.R., “Additional results concerning estimable functions and generalized inverse matrices”, J. Roy. Statist. Soc. Ser. B 27 (1965), 486–490.
[8]Urquhart, N.S., “Computation of generalized inverse matrices which satisfy specified conditions”, SIAM Rev. 10 (1968), 216–218.
[9]Urguhart, N.S. and Williams, J.S., “A multivariate test of significance for responses from any population I: Unrestricted randomization” (Biometrics Unit Mimeo, Ser. No. BU-156, 1967. Cornell University, Ithaca, New York, 1967).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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