Definitions for self-adjoint
self-ad·joint

WiktionaryRate this definition:0.0 / 0 votes

1. self-adjointadjective

   which is adjoint to itself

WikipediaRate this definition:0.0 / 0 votes

1. Self-adjoint

   In mathematics, and more specifically in abstract algebra, an element x of a *-algebra is self-adjoint if x ∗ = x {\displaystyle x^{*}=x} . A self-adjoint element is also Hermitian, though the reverse doesn't necessarily hold. A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation. For example, if x ∗ = y {\displaystyle x^{*}=y} then since y ∗ = x ∗ ∗ = x {\displaystyle y^{*}=x^{**}=x} in a star-algebra, the set {x,y} is a self-adjoint set even though x and y need not be self-adjoint elements. In functional analysis, a linear operator A : H → H {\displaystyle A:H\to H} on a Hilbert space is called self-adjoint if it is equal to its own adjoint A∗. See self-adjoint operator for a detailed discussion. If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator A is self-adjoint if and only if the matrix describing A with respect to this basis is Hermitian, i.e. if it is equal to its own conjugate transpose. Hermitian matrices are also called self-adjoint. In a dagger category, a morphism f {\displaystyle f} is called self-adjoint if f = f † {\displaystyle f=f^{\dagger }} ; this is possible only for an endomorphism f : a → a {\displaystyle f\colon a\to a} .

WikidataRate this definition:4.0 / 1 vote

1. Self-adjoint

   In mathematics, an element x of a star-algebra is self-adjoint if . A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation. For example, if then since in a star-algebra, the set {x,y} is a self-adjoint set even though x and y need not be self-adjoint elements. In functional analysis, a linear operator A on a Hilbert space is called self-adjoint if it is equal to its own adjoint A* and that the domain of A is the same as that of A*. See self-adjoint operator for a detailed discussion. If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator A is self-adjoint if and only if the matrix describing A with respect to this basis is Hermitian, i.e. if it is equal to its own conjugate transpose. Hermitian matrices are also called self-adjoint.

How to pronounce self-adjoint?

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Numerology

1. Chaldean Numerology

   The numerical value of self-adjoint in Chaldean Numerology is: 6

2. Pythagorean Numerology

   The numerical value of self-adjoint in Pythagorean Numerology is: 7

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Self-Adjoint
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Self-Adjoint
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=self-adjoint