|
|
| Line 1: |
Line 1: |
| In [[mathematics]], an element ''x'' of a [[star-algebra]] is '''self-adjoint''' if <math>x^*=x</math>.
| |
|
| |
|
| A collection ''C'' of elements of a star-algebra is '''self-adjoint''' if it is closed under the [[Involution (mathematics)|involution]] operation. For example, if <math>x^*=y</math> then since <math>y^*=x^{**}=x</math> 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 operator|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 (mathematics)|matrix]] describing ''A'' with respect to this basis is [[Hermitian matrix|Hermitian]], i.e. if it is equal to its own [[conjugate transpose]]. Hermitian matrices are also called '''self-adjoint'''.
| | Custom. The author's name is Dalton but nonetheless , it's not the almost all masucline name out high. To drive is one of a [http://Www.dict.cc/?s=person%27s person's] things he loves the [https://Www.Google.com/search?hl=en&gl=us&tbm=nws&q=vast+majority&btnI=lucky vast majority]. His wife and him chose to live on in South Carolina additionally his family loves the following. Auditing is even his primary income comes from. He 's running and maintaining one specific blog here: http://prometeu.net<br><br>My site ... [http://prometeu.net clash of clans hack cydia source] |
| | |
| ==See also==
| |
| *[[Symmetric matrix]]
| |
| *[[Hermitian]]
| |
| | |
| ==References==
| |
| *{{cite book |authorlink=Michael C. Reed |first=M. |last=Reed |authorlink2=Barry Simon |first2=B. |last2=Simon |title=Methods of Mathematical Physics |others=Vol 2 |publisher=Academic Press |year=1972 |isbn= }}
| |
| *{{cite book |authorlink=Gerald Teschl |first=G. |last=Teschl |title=Mathematical Methods in Quantum Mechanics; With Applications to Schrödinger Operators |publisher=American Mathematical Society |location=Providence |year=2009 |url=http://www.mat.univie.ac.at/~gerald/ftp/book-schroe/ }}
| |
| | |
| | |
| {{DEFAULTSORT:Self-Adjoint}}
| |
| [[Category:Abstract algebra]]
| |
| [[Category:Linear algebra]]
| |
Latest revision as of 16:43, 25 December 2014
Custom. The author's name is Dalton but nonetheless , it's not the almost all masucline name out high. To drive is one of a person's things he loves the vast majority. His wife and him chose to live on in South Carolina additionally his family loves the following. Auditing is even his primary income comes from. He 's running and maintaining one specific blog here: http://prometeu.net
My site ... clash of clans hack cydia source