Definition:Orthogonal Matrix/Definition 2

Definition
Let $R$ be a ring with unity.

Let $\mathbf Q$ be an invertible square matrix over $R$.

Then $\mathbf Q$ is orthogonal :
 * $\mathbf Q^\intercal \mathbf Q = \mathbf I$

where:
 * $\mathbf Q^\intercal$ is the transpose of $\mathbf Q$
 * $\mathbf I$ is the identity matrix of the same order as $\mathbf Q$.

Also see

 * Equivalence of Definitions of Orthogonal Matrix