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An identity for the Schur complement of a matrix


Authors: Douglas E. Crabtree and Emilie V. Haynsworth
Journal: Proc. Amer. Math. Soc. 22 (1969), 364-366
MSC: Primary 15.20
DOI: https://doi.org/10.1090/S0002-9939-1969-0255573-1
MathSciNet review: 0255573
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References [Enhancements On Off] (What's this?)

  • [1] Douglas E. Crabtree, Applications of M-matrices to nonnegative matrices, Duke Math. J. 33 (1966), 197-208. MR 0186677 (32:4135)
  • [2] -, Characteristic roots of M-matrices, Proc. Amer. Math. Soc. 17 (1966), 1435-1439. MR 0199203 (33:7352)
  • [3] -, A matrix identity, Amer. Math. Monthly 75 (1968), 648-649. MR 0229663 (37:5237)
  • [4] F. R. Gantmacher, The theory of matrices, Vol. 1, Chelsea, New York, 1959, p. 33. MR 1657129 (99f:15001)
  • [5] Emilie V. Haynsworth, Determination of the inertia of a partitioned Hermitian matrix, Linear Algebra and Appl. 1 (1968), 73-81. MR 0223392 (36:6440)

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DOI: https://doi.org/10.1090/S0002-9939-1969-0255573-1
Article copyright: © Copyright 1969 American Mathematical Society

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