Rylan Schaeffer

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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.

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