Definition:Orthogonal Matrix/Definition 1
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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:
- $\mathbf Q^{-1} = \mathbf Q^\intercal$
where:
- $\mathbf Q^{-1}$ is the inverse of $\mathbf Q$
- $\mathbf Q^\intercal$ is the transpose of $\mathbf Q$
Also see
- Results about orthogonal matrices can be found here.
Sources
- 1980: A.J.M. Spencer: Continuum Mechanics ... (previous) ... (next): $2.1$: Matrices: $(2.11)$