Self-adjoint
Self-adjoint In mathematics, an element x of a star-algebra is self-adjoint if $x^*=x$. A collection ... of elements of a star-algebra is self-adjoint if it is closed under ...
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Talk:Self-adjoint
Talk:Self-adjoint A simpler definition? An operator T∈L(V) is called self-adjoint iff T = T*. Well, that's what ... is a star-algebra and T*, the adjoint of T, is the image of ...
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Self-adjoint operator
Self-adjoint operator On a finite-dimensional inner product space, a self-adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is ...
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Talk:Self-adjoint operator
Talk:Self-adjoint operator The latest anonymous "edit" intorduces a ...
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Hermitian adjoint
Hermitian adjoint In mathematics, specifically in functional analysis, one ... linear operator on a Hilbert space its adjoint operator. Adjoints of operators generalize conjugate transposes ... space as "generalized complex numbers", then the adjoint of an operator plays the role of ... complex conjugate of a complex number. The adjoint of an operator A is also sometimes called the Hermitian adjoint of A and is denoted by ...
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Borel functional calculus
... apply an arbitrary Borel function to a self-adjoint operator, in a way which generalizes applying ... polynomial function. Motivation If T is a self-adjoint operator on a finite dimensional inner product ... lambda_k) e_k. \quad In general, any self-adjoint operator T is unitarily equivalent ...
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Spectral theorem
... to which the spectral theorem applies are self-adjoint operators or more generally normal operators on ... kind of spectral theorem, that for a self-adjoint operator on a Hilbert space. However, as ... are real. The spectral theorem for compact self-adjoint operators In Hilbert spaces in ...
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Friedrichs extension
... analysis, the Friedrichs extension is a canonical self-adjoint extension of a non-negative densely defined ... an operator may fail to be essentially self-adjoint or whose essential self-adjointness is difficult to show. An ...
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Quantum logic
... is familiar with the spectral theory of self-adjoint operators on a Hilbert space. However, the ... represented by some (possibly unbounded) densely-defined self-adjoint operator A on a Hilbert space H ... b], the operator f(A) is a self-adjoint projection, and can be interpreted ...
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C*-algebra
... A is the set of minimal nonzero self-adjoint central projections of A. Each C*-algebra ... Hilbert space H; here x* denotes the adjoint operator of the operator x : H → ... A is *-isomorphic to a norm-closed adjoint closed subalgebra of L(H) for a ... C*-algebra A with unit element; the self-adjoint elements of A (elements x ...
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