Definition:Orthogonal Matrix

Definition
Let $R$ be a ring with unity.

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

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

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

Also see

 * Definition:Orthogonal Group
 * Definition:Unitary Matrix
 * Definition:Symmetric Matrix