Factorizations of nonnegative matrices
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- by T. L. Markham PDF
- Proc. Amer. Math. Soc. 32 (1972), 45-47 Request permission
Abstract:
Suppose A is an n-square matrix over the real numbers such that all principal minors are nonzero. If A is nonnegative, then necessary and sufficient conditions are determined for A to be factored into a product $L \cdot U$, where L is a lower triangular nonnegative matrix and U is an upper triangular nonnegative matrix with ${u_{ii}} = 1$. These conditions are given in terms of the nonnegativity of certain almost-principal minors of A.References
- Douglas E. Crabtree and Emilie V. Haynsworth, An identity for the Schur complement of a matrix, Proc. Amer. Math. Soc. 22 (1969), 364–366. MR 255573, DOI 10.1090/S0002-9939-1969-0255573-1 F. R. Gantmacher, The theory of matrices. Vol. 2, Chelsea, New York, 1959. MR 21 #6372c.
- Emilie V. Haynsworth, Determination of the inertia of a partitioned Hermitian matrix, Linear Algebra Appl. 1 (1968), no. 1, 73–81. MR 223392, DOI 10.1016/0024-3795(68)90050-5
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 45-47
- MSC: Primary 15.60
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289539-2
- MathSciNet review: 0289539