This is a Linear Algebra Question Exercise 1009 Let n be a p

This is a Linear Algebra Question

Exercise 1009 Let n be a positive integer. A matrix A Lai E Mnxin (C) is a complex Hadamard matrix if and only if lahj 1 for all 1 S h, j S n and any pair of distinct rows of A, considered as vectors in Cn is orthogonal. For each n, find a complex number d such that A hij is a complex Hadamard matrix. For n 6, find a complex Hadamard matrix which is not of this form.

Solution

the complex Hadamard matrix which is not of this form is

aij = 6

A = [ 6,6,6,6,6,6]