Additive decomposition of nonnegative matrices with applications to permanents and scalingt
- 1 March 1988
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 23 (1) , 63-78
- https://doi.org/10.1080/03081088808817857
Abstract
Let U1 and U2 be compact subsets of m × n nonnegative matrices with prescribed row sums and column sums. Given A in U2 , we study the quantity and the matrices B in U1 that satisfy A−μ(U1;A)B is nonnegative.The quantity is determined. Using the results obtained, we give a lower bound for the permanent of nonnegative matrices. Moreover, we study the scaling parameters of nonnegative matrices. An upper bound and an extremal characterization for their product are given.Keywords
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