adjoint operator
61Hellinger–Toeplitz theorem — In functional analysis, a branch of mathematics, the Hellinger–Toeplitz theorem states that an everywhere defined symmetric operator on a Hilbert space is bounded. By definition, an operator A is symmetric if : langle A x | y angle = langle x | A …
62Sturm-Liouville theory — In mathematics and its applications, a classical Sturm Liouville equation, named after Jacques Charles François Sturm (1803 1855) and Joseph Liouville (1809 1882), is a real second order linear differential equation of the formwhere y is a… …
63Weitzenböck identity — In mathematics, in particular in differential geometry, mathematical physics, and representation theory a Weitzenbock identity expresses a relationship between two second order elliptic operators on a manifold with the same leading symbol.… …
64Quantum statistical mechanics — is the study of statistical ensembles of quantum mechanical systems. A statistical ensemble is described by a density operator S , which is a non negative, self adjoint, trace class operator of trace 1 on the Hilbert space H describing the… …
65Polar 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… …
66Riemann hypothesis — The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011 …
67Eigenvalues 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… …
68Eigenvalue, 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… …
69Coercive function — In mathematics, a coercive function is a function that grows rapidly at the extremes of the space on which it is defined. More precisely, a function f : Rn → Rn is called coercive if where denotes the usual dot product and denotes the usual… …
70Hamburger moment problem — In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence { αn : n = 1, 2, 3, ... }, does there exist a positive Borel measure μ on the real line such that:alpha n = int {… …
