Almost Hadamard Matrices: General Theory and Examples-Reference-Cited by-同舟云学术

Almost Hadamard Matrices: General Theory and Examples

Published:2012-12 Issue:04 Volume:19 Page:1250024
ISSN:1230-1612
Container-title:Open Systems & Information Dynamics
language:en
Short-container-title:Open Syst. Inf. Dyn.

Author:

Banica Teodor¹,Nechita Ion²,Życzkowski Karol³

Affiliation:

1. Department of Mathematics, Cergy-Pontoise University, 95000 Cergy–Pontoise, France

2. CNRS, Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, UPS, 31062, Toulouse, France

3. Institute of Physics, Jagiellonian University, Cracow and Center for Theoretical Physics, Polish Academy of Sciences, Warsaw, Poland

Abstract

We develop a general theory of almost Hadamard matrices. These are by definition the matrices H ∈ MN(ℝ) having the property that [Formula: see text] is orthogonal, and is a local maximum of the 1-norm on O (N). Our study includes a detailed discussion of the circulant case (Hij= γj-i) and of the two-entry case (Hij∈ {x, y}), with the construction of several families of examples, and some 1-norm computations.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1230161212500242

Reference33 articles.

1. Error Correcting Codes from Quasi-Hadamard Matrices

2. Quantum automorphism groups of homogeneous graphs

3. Representations of quantum permutation algebras

4. On orthogonal matrices maximizing the 1-norm

5. On polynomial integrals over the orthogonal group

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