Accession Number : ADA182264

Title :   Matrix Theory.

Descriptive Note : Annual rept. 1 Jul 86-30 Jun 87,

Corporate Author : CALIFORNIA UNIV SANTA BARBARA DEPT OF MATHEMATICS

Personal Author(s) : Minc, Henryk

PDF Url : ADA182264

Report Date : 30 Jun 1987

Pagination or Media Count : 5

Abstract : Two areas of matrix theory are discussed: the theory of permanents, and the theory of nonnegative matrices. Paper (1) deals with permanental compounds and their use in recurrence formulas for permanents of (0,1)-circulants and in related asymptotic formulas. Paper (2) is a extensive survey of the progress in the theory of permanents achieved during the quadrennium 1982-1985. Paper (3) deals with the problem of determining the minimum permanent in the set of n x n doubly stochastic matrices whose first main diagonal entries are equal to zero. The case k = o is the famed van der Waerden conjecture. The case k = 1 can be easily solved by a method similar to that used by Egorycev in proving the van der Waerden conjecture. For k = 2 Egorycev's techniques are of limited use. The case was solved by me in 1984. For 3 or - n the problem is still unsolved.

Descriptors :   *MATRIX THEORY, ASYMPTOTIC SERIES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE