Entropy of Orthogonal Matrices and Minimum Distance Orthostochastic Matrices From the Uniform Van Der Waerden Matrices
Document Type
Article
Publication Date
2-2019
Abstract
In this article we formulate an optimization problem of minimizing the distance from the uniform van der Waerden matrices to orthostochastic matrices of different orders. We find a lower bound for the number of stationary points of the minimization problem, which is connected to the number of possible partitions of a natural number. The existence of Hadamard matrices ensures the existence of global minimum orthostochastic matrices for such problems. The local minimum orthostochastic matrices have been obtained for all other orders except for 11 and 19. We explore the properties of Hadamard, conference and weighing matrices to obtain such minimizing orthostochastic matrices.
Repository Citation
Arasu, K. T.
(2019). Entropy of Orthogonal Matrices and Minimum Distance Orthostochastic Matrices From the Uniform Van Der Waerden Matrices. Discrete Optimization, 31, 115-144.
https://corescholar.libraries.wright.edu/math/328
DOI
10.1016/j.disopt.2018.10.001
