self-adjoint
41Eigenvalue, eigenvector and eigenspace — In mathematics, given a linear transformation, an Audio|De eigenvector.ogg|eigenvector of that linear transformation is a nonzero vector which, when that transformation is applied to it, changes in length, but not direction. For each eigenvector… …
42Kaplansky density theorem — In the theory of von Neumann algebras, the Kaplansky density theorem states thatif A is a * subalgebra of the algebra B ( H ) of bounded operators on a Hilbert space H , then the strong closure of the unit ball of A in B ( H ) is the unit ball of …
43Eigenvalues and eigenvectors — For more specific information regarding the eigenvalues and eigenvectors of matrices, see Eigendecomposition of a matrix. In this shear mapping the red arrow changes direction but the blue arrow does not. Therefore the blue arrow is an… …
44Von Neumann algebra — In mathematics, a von Neumann algebra or W* algebra is a * algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann,… …
45Von Neumann bicommutant theorem — In mathematics, the von Neumann bicommutant theorem in functional analysis relates the closure of a set of bounded operators on a Hilbert space in certain topologies to the bicommutant of that set. In essence, it is a connection between the… …
46Min-max theorem — Variational theorem redirects here. The term is also sometimes applied to the variational principle. In linear algebra and functional analysis, the min max theorem, or variational theorem, or Courant–Fischer–Weyl min max principle, is a result… …
47Superselection sector — A superselection sector is a concept used in quantum mechanics when a representation of a * algebra is decomposed into irreducible components. It formalizes the idea that not all self adjoint operators are observables because the relative phase… …
48Stone's theorem on one-parameter unitary groups — In mathematics, Stone s theorem on one parameter unitary groups is a basic theorem of functional analysis which establishes a one to one correspondence between self adjoint operators on a Hilbert space H and one parameter families of unitary… …
49Projection-valued measure — In mathematics, particularly functional analysis a projection valued measure is a function defined on certain subsets of a fixed set and whose values are self adjoint projections on a Hilbert space. Projection valued measures are used to express… …
50Polar decomposition — In mathematics, particularly in linear algebra and functional analysis, the polar decomposition of a matrix or linear operator is a factorization analogous to the polar form of a nonzero complex number z where r is the absolute value of z (a… …
