nLab
unitary matrix

An n×nn \times n-matrix UMat(n,)U \in Mat(n, \mathbb{C}) with entries in the complex numbers (for nn a natural number) is unitary if the following equivalent conditions hold

  • it preserves the canonical inner product on n\mathbb{C}^n;

  • the operation () (-)^\dagger of transposing it and then applying complex conjugation to all its entries takes it to its inverse:

    U =U 1. U^\dagger = U^{-1} \,.

For fixed nn, the unitary matrices under matrix product form a Lie group: the unitary group U(n)\mathrm{U}(n) (or other notations).

Last revised on January 22, 2013 at 14:57:18. See the history of this page for a list of all contributions to it.