Self Adjoint

In mathematics, an element x of a star-algebra is self-adjoint if the involution acts trivially upon it. In other words, . When we work in an inner product space which is a star-algebra, being self-adjoint is the same as being hermitian.

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 linear algebra, an operator T∈L(V) is called self-adjoint iff T = T*.

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