The theory and applications of complex matrix scalings

• Autorzy: Rajesh Pereira , Joanna Boneng
• Języki publikacji: EN

Abstrakty

EN

We generalize the theory of positive diagonal scalings of real positive definite matrices to complex diagonal scalings of complex positive definite matrices. A matrix A is a diagonal scaling of a positive definite matrix M if there exists an invertible complex diagonal matrix D such that A = D*MD and where every row and every column of A sums to one. We look at some of the key properties of complex diagonal scalings and we conjecture that every n by n positive definite matrix has at most 2n−1 scalings and prove this conjecture for certain special classes of matrices.We also use the theory of complex diagonal matrix scalings to formulate a van der Waerden type question on the permanent function; we show that the solution of this question would have applications to finding certain maximally entangled quantum states.

Słowa kluczowe

EN

Diagonal Matrix Scalings; Positive Definite Matrices; Circulant Matrices; Tridiagonal Matrices; Doubly Stochastic Matrices; Permanent; Symmetric States; Geometric Measure of Entanglement

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2014
• Tom: 2
• Numer: 1
• Strony: 68-77

Daty

wydano

2014-01-01

otrzymano

2013-12-05

zaakceptowano

2014-04-13

online

2014-05-17

Twórcy

autor

Rajesh Pereira

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

autor

Joanna Boneng

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

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Identyfikatory

DOI

10.2478/spma-2014-0007