How to Use it 

This program allows you to generate Hadamard matrix of orders up to 1000.

What is a Hadamard matrix?

A Hadamard matrix H is a square matrix of order n with all its entries as +1 and -1 such that HH' = H'H = nI, where I is a square matrix of order n. It is well known that Hadamard matrix exists whenever n=1,2 or a multiple of 4. It is also conjectured that Hadamard matrix exists for all multiples of 4. The least order for which Hadamard matrix construction is unknown is 668.

How to use the program?

Fill the form and click on submit button to generate the required Hadamard matrix. 

Order (required) 

Enter the order of the Hadamard matrix required

Normalization

A Hadamard matrix is said to be in semi-Normalized form, if all its first row or first column consist of entirely "+1"s. If both first row as well as first column consist of "+1"s, then it is said to be in Normalized form. Use this option if you want the Hadamard matrix in semi-normalized form or normalized form or none (which is default). Note that some construction methods result in Normalized form.

Output

Three different types of outputs are possible. The first option "+1 & -1", which is default produces the usual Hadamard matrices. The second option, "+ & -", replaces "1" as "+" and "-1" as "-" and the third option replaces "-1" as "0". The first option may be slow in display as compared to second and third options. Also, in the first options, rows may be break in to more than one line. Use the second or third option for faster outputs.