On the cardinality of complex matrix scalings

• Autorzy: George Hutchinson
• Języki publikacji: EN

Abstrakty

EN

We disprove a conjecture made by Rajesh Pereira and Joanna Boneng regarding the upper bound on the number of doubly quasi-stochastic scalings of an n × n positive definite matrix. In doing so, we arrive at the true upper bound for 3 × 3 real matrices, and demonstrate that there is no such bound when n ≥ 4.

Słowa kluczowe

EN

Diagonal Matrix Scalings; Positive Definite Matrices; Circulant Matrices; Doubly Stochastic Matrices

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 141-150

Daty

otrzymano

2015-11-13

zaakceptowano

2016-01-30

online

2016-02-22

Twórcy

autor

George Hutchinson

• Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1.

Bibliografia

• [1] R. Sinkhorn. A relationship between arbitrary positive matrices and doubly stochastic matrices. Annals of Mathematical Statistics, 35(2):876–879, 1964. [Crossref]
• [2] A.W. Marshall and I. Olkin. Scaling of matrices to achieve specified row and column sums. Numer. Math., 12(1):83–90, 1968. [Crossref]
• [3] M. V. Menon. Reduction of amatrix with positive elements to a doubly stochasticmatrix. Proc. Amer.Math. Soc., 18:244–247, 1967. [Crossref]
• [4] R. Brualdi, S. Parter, and H. Schneider. The diagonal equivalence of a non-negative matrix to a stochastic matrix. J. Math. Anal. Appl., 16:31–50, 1966. [Crossref]
• [5] C. R. Johnson and R. Reams. Scaling of symmetric matrices by positive diagonal congruence. Linear Multilinear Algebra, 57:123–140, 2009. [Crossref]
• [6] R. Pereira and J. Boneng. The theory and applications of complex matrix scalings, Spec. Matrices, 2: 68-77, 2014
• [7] P. J. Davis. Circulant Matrices. John Wiley & Sons, 1979.
• [8] D. P. O’Leary. Scaling symmetric positive definite matrices to prescribed row sums. Linear Algebra Appl., pages 185–191, 2003.

Identyfikatory

DOI

10.1515/spma-2016-0014