Category:Orthogonal Matrices

This category contains results about Orthogonal Matrices.

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 $\mathbf Q$