Lumped element model

In mathematics, an element x of a star-algebra is self-adjoint if $x^{*}=x$.

A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation. For example, if $x^{*}=y$ then since $y^{*}=x^{**}=x$ 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 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.

See also

• Symmetric matrix
• Hermitian

References

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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534