What does unitary operator mean?
Definitions for unitary operator
uni·ta·ry op·er·a·tor
This dictionary definitions page includes all the possible meanings, example usage and translations of the word unitary operator.
Wikipedia
Unitary operator
In functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually taken as operating on a Hilbert space, but the same notion serves to define the concept of isomorphism between Hilbert spaces. A unitary element is a generalization of a unitary operator. In a unital algebra, an element U of the algebra is called a unitary element if U*U = UU* = I, where I is the identity element.
Wikidata
Unitary operator
In functional analysis, a branch of mathematics, a unitary operator is defined as follows: Definition 1. A bounded linear operator U : H → H on a Hilbert space H is called a unitary operator if it satisfies U*U = UU* = I, where U* is the adjoint of U, and I : H → H is the identity operator. The weaker condition U*U = I defines an isometry. The other condition, UU* = I, defines a coisometry. Thus a unitary operator is a bounded linear operator which is both an isometry and a coisometry. An equivalent definition is the following: Definition 2. A bounded linear operator U : H → H on a Hilbert space H is called a unitary operator if: U is surjective, and U preserves the inner product of the Hilbert space, H. In other words, for all vectors x and y in H we have: The following, seemingly weaker, definition is also equivalent: Definition 3. A bounded linear operator U : H → H on a Hilbert space H is called a unitary operator if: the range of U is dense in H, and U preserves the inner product of the Hilbert space, H. In other words, for all vectors x and y in H we have: To see that Definitions 1 & 3 are equivalent, notice that U preserving the inner product implies U is an isometry.
Numerology
Chaldean Numerology
The numerical value of unitary operator in Chaldean Numerology is: 2
Pythagorean Numerology
The numerical value of unitary operator in Pythagorean Numerology is: 9
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"unitary operator." Definitions.net. STANDS4 LLC, 2024. Web. 28 Mar. 2024. <https://www.definitions.net/definition/unitary+operator>.
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