Overview

# unitary transformation

## Quick Reference

A transformation that has the form *O*′ = *UOU*^{−1}, where *O* is an operator, *U* is a unitary matrix and *U*^{−1} is its reciprocal, i.e. if the matrix obtained by interchanging rows and columns of *U* and then taking the complex conjugate of each entry, denoted *U*^{+}, is the inverse of *U*; *U*^{+} = *U*^{−1}. The inverse of a unitary transformation is itself a unitary transformation. Unitary transformations are important in quantum mechanics. In the Hilbert space formulation of states in quantum mechanics a unitary transformation corresponds to a rotation of axes in the Hilbert space. Such a transformation does not alter the state vector, but a given state vector has different components when the axes are rotated.

*Subjects:*
Science and technology
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Physics