Definition:Orthogonal Matrix/Definition 3
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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:
- $\mathbf Q = \paren {\mathbf Q^\intercal}^{-1}$
where:
- $\mathbf Q^\intercal$ is the transpose of $\mathbf Q$
- $\paren {\mathbf Q^\intercal}^{-1}$ is the inverse of $\mathbf Q^\intercal$.
Also see
- Results about orthogonal matrices can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): orthogonal matrix
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): orthogonal matrix