Definition:Orthogonal Matrix/Definition 2

This page is about Orthogonal Matrix. For other uses, see Orthogonal.

Definition

Let $R$ be a ring with unity.

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

Then $\mathbf Q$ is orthogonal if and only if:

$\mathbf Q^\intercal \mathbf Q = \mathbf I$

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

• Results about orthogonal matrices can be found here.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): orthogonal matrix