Definition:Hadamard Matrix/Definition 2

Definition
A Hadamard matrix $H$ is a square matrix such that:
 * $(1): \quad$ all the entries of $H$ are either $+1$ or $-1$
 * $(2): \quad H H^\intercal = n \mathbf I$

where:
 * $H^\intercal$ denotes the transpose of $H$
 * $\mathbf I$ denotes the identity matrix of order $n$.

Also see

 * Equivalence of Definitions of Hadamard Matrix