# 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.

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