Random Generation of Binary Orthogonal Matrix of Size n * n with Matlab

Dear all...

How can I generate random binary orthogonal matrix of size n * n with matlab?

Regards,

Answer 1

[Guillaume]

I'm not a mathematician so I could be completely wrong but aren't square binary orthogonal matrices just permutations of the rows (or columns) of the identity matrix?

If yes,

m = eye(n);
m = m(randperm(n), :)

This certainly generates random binary orthogonal matrices of size nxn. Whether it can generate all the possible ones, I don't know.

[Hiba Basim Alwan]

Thank you so much for your helping.

[Uri Cohen]

No, they are not.

Answer 2

[javad ebrahimi]

Hi Hiba Basim Alwan

this code can help you: for n=10

C = rand(10)
Y = round(C)

[Guillaume]

That does produce a matrix that is binary and random, but certainly not orthogonal (which is the difficult bit of the question).

randi([0 1], n)

is a simpler way of producing a binary matrix.