Unitary element

In mathematics, an element x of a *-algebra is unitary if it satisfies

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.

See also

References
    • Reed, M.; Simon, B. (1972). Methods of Mathematical Physics. Vol 2. Academic Press.
    • Teschl, G. (2009). Mathematical Methods in Quantum Mechanics; With Applications to Schrödinger Operators. Providence: American Mathematical Society.
    • Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.
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