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On the cardinality of complex matrix scalings

100%

Hutchinson G.

Special Matrices

2016

tom 4

nr 1

141-150

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.

The theory and applications of complex matrix scalings

63%

Pereira R., Boneng J.

Special Matrices

2014

tom 2

nr 1

68-77

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.

Ograniczanie wyników

2 Special Matrices

1 Boneng J.

1 Hutchinson G.

1 Pereira R.

1 2016

1 2014

Wyniki wyszukiwania

On the cardinality of complex matrix scalings

The theory and applications of complex matrix scalings