Significant Properties and Examples of Unitary Matrices

Abstract

This article surveys significant properties and examples of unitary matrices. Various characterizations of unitary matrices, involving algebraic properties and properties related to orthogonality, inner products, norms and eigenvalues, are provided. We consider groups of unitary matrices and their important subgroups. Practical examples of unitary matrices are rotations, reflections, Householder reflections and matrices which represent quantum gates.