About the problem

A Hadamard matrix is a square matrix all of whose entries are \(\pm 1\) and whose rows are mutually orthogonal. Beyond trivial cases, the order of such a matrix must be a multiple of four. The Hadamard conjecture states that a Hadamard matrix exists for every such order. It remains open.

Mathematicians have chipped away at finding examples of Hadamard matrices of larger and larger order. The smallest case for which no matrix is known is \(668\). The previous smallest unknown case was \(428\), resolved in 2004 by Kharaghani and Tayfeh-Rezaie. New cases typically require somewhat clever and novel constructions.

This problem asks for a Hadamard matrix of order \(668\).

Prompt

Find a Hadamard matrix of order 668.

Write your Hadamard matrix to an .npy file (using `numpy.save`) and output the filepath. The matrix must be a square array of +1 and -1 entries.