Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Factorizations of nonnegative matrices

Author: T. L. Markham
Journal: Proc. Amer. Math. Soc. 32 (1972), 45-47
MSC: Primary 15.60
MathSciNet review: 0289539
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] D. E. Crabtree and E. V. Haynsworth, An identity for the Schur complement of a matrix, Proc. Amer. Math. Soc. 22 (1969), 364-366. MR 41 #234. MR 0255573 (41:234)
  • [2] F. R. Gantmacher, The theory of matrices. Vol. 2, Chelsea, New York, 1959. MR 21 #6372c.
  • [3] E. V. Haynsworth, Determination of the inertia of a partitioned Hermitian matrix, Linear Algebra and Appl. 1 (1968), no. 1, 73-81. MR 36 #6440. MR 0223392 (36:6440)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15.60

Retrieve articles in all journals with MSC: 15.60

Additional Information

Keywords: Factorization, nonnegative matrix, almost principal minor, lower triangular matrix, upper triangular matrix
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society