- Self-adjoint
In

mathematics , an element "x" of astar-algebra is**self-adjoint**if $x^*=x$.A collection "C" of elements of a star-algebra is

**self-adjoint**if it is closed under theinvolution 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 , alinear operator "A" on aHilbert space is called**self-adjoint**if it is equal to its own adjoint "A"*. Seeself-adjoint operator for a detailed discussion. If the Hilbert space is finite-dimensional and anorthonormal 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 ownconjugate transpose . Hermitian matrices are also called**self-adjoint**.**ee also***

symmetric matrix

*Hermitian

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