A characterization of Hadamard matrices
Any Hadamard matrix of order \(n=4t\) can be given the form \(H=\left(\begin{smallmatrix} J&J&A\\ J&-J&B\end{smallmatrix}\right),\) where \(J\) is the column vector of length \(n/2=2t\) with all entries \(+1.\) The paper presents an elementary proof for the fact, that the other three matrices \(\left(\begin{smallmatrix} J&J&\pm A\\ J&-J&\pm B\end{smallmatrix}\right)\) are then Hadamard matrices as well.
scientific article; zbMATH DE number 1347329