Unitary Operator

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Unitary Operator

 

an extension of the notation of a rotation of Euclidean space to the infinite-dimensional case. More precisely, a unitary operator is a rotation of a Hilbert space about the origin. In analytic terms, an operator U that maps the Hilbert space H onto itself is said to be unitary if (f, g) = (Uf,Ug) for any two vectors f, g in H. A unitary operator preserves lengths of vectors and angles between vectors and is a linear operator. A unitary operator U has a unitary inverse U–1 such that U–1 = U*, where U* is the adjoint of U.

An example of a unitary operator is the Fourier-Plancherel operator, which associates to each function f(x), – ∞ < x < ∞, with square integrable absolute value the function

References in periodicals archive ?
This technical (syntactic) tool, which originates in early transformational-generative grammar but is fully developed in recent versions of the Chomskyan Minimalist Program, might be interpreted as an operation that creates objects within objects, a single unitary operation combining structure building and movement.
Granulation is a widely applied unitary operation, especially in the pharmaceutical and chemical industries, with operators sharing the common goal of controlling particle size to meet granulate performance goals.
Since the set of unitary operations is continuous, it is clear that a discrete set of gates is not sufficient to implement an arbitrary unitary operation.
Now, it can be shown that the discrete set of quantum gates formed by the normalizer group, plus the Toffoli gate is universal for quantum computation; that is an arbitrary unitary operation on d qubits can be approximated to an arbitrary accuracy using a circuit composed only from these gates.
Hence, Mohasco functioned as part of a single unitary operation with Carpet.
The process incorporates sustainability in all the steps that are critical for extraction: choice of the solvent or technologies, utilization of by-products, reduction of unitary operations, and limitation of chemical alteration of botanical extracts.
He also taught courses in thermodynamics and unitary operations and processes.