Definition:Orthogonal Matrix/Definition 2
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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
- 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