On Agaian Matrix

TL;DR

This paper investigates the Agaian matrix, a 6-dimensional complex Hadamard matrix, demonstrating its isolation property due to its high symmetry, regardless of the equivalence method used.

Contribution

It proves that the Agaian matrix is isolated among 6-dimensional complex Hadamard matrices, highlighting its symmetry as a key factor.

Findings

Agaian matrix is isolated among 6-dimensional matrices

High symmetry of the matrix leads to its isolation

Both equivalence methods confirm the isolation

Abstract

In this paper we discuss the isolation problem of the Agaian matrix among the 6-dimensional matrices. In general a matrix isolation could depend on the kind of equivalence one uses for complex Hadamard matrices. However the present form of Agaian matrix has such a big symmetry that both equivalence methods lead to the same result: the matrix is isolated.