Definition:Orthogonal Matrix/Definition 3

Definition
Let $R$ be a ring with unity.

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

Then $\mathbf Q$ is orthogonal :
 * $\mathbf Q = \paren {\mathbf Q^\intercal}^{-1}$

where:
 * $\mathbf Q^\intercal$ is the transpose of $\mathbf Q$
 * $\paren {\mathbf Q^\intercal}^{-1}$ is the inverse of $\mathbf Q^\intercal$.

Also see

 * Equivalence of Definitions of Orthogonal Matrix