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# Linear Algebra

## Unitary (Orthogonal) Matrices

A square matrix is unitary if its transpose is its inverse i.e. $$U^{-1} = U^T$$. One key utility of unitary matrices is that they leave the dot product invariant i.e.

$\langle U x, U y \rangle = \langle U{-1} U x, y \rangle = \langle U^T U x, y \rangle = \langle x, y \rangle$