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In mathematics, an element x of a *-algebra is unitary if it satisfies x ∗ = x − 1 . {\displaystyle x^{*}=x^{-1}.}
In functional analysis, a linear operator A from a Hilbert space into itself is called unitary if it is invertible and its inverse is equal to its own adjoint A and that the domain of A is the same as that of A. See unitary operator for a detailed discussion. If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator A is unitary if and only if the matrix describing A with respect to this basis is a unitary matrix.
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