self-adjoint family
1Self-adjoint operator — In mathematics, on a finite dimensional inner product space, a self adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose.… …
2Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …
3Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …
4Decomposition of spectrum (functional analysis) — In mathematics, especially functional analysis, the spectrum of an operator generalizes the notion of eigenvalues. Given an operator, it is sometimes useful to break up the spectrum into various parts. This article discusses a few examples of… …
5C*-algebra — C* algebras (pronounced C star ) are an important area of research in functional analysis, a branch of mathematics. The prototypical example of a C* algebra is a complex algebra A of linear operators on a complex Hilbert space with two additional …
6Quantum logic — In mathematical physics and quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles of quantum theory into account. This research area and its name originated in the 1936 paper by Garrett… …
7Hamburger 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 {… …
8Coherent states in mathematical physics — Coherent states have been introduced in a physical context, first as quasi classical states in quantum mechanics, then as the backbone of quantum optics and they are described in that spirit in the article Coherent states (see also [1]). However …
9Atiyah–Singer index theorem — In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) …
10Density matrix — Mixed state redirects here. For the psychiatric condition, see Mixed state (psychiatry). In quantum mechanics, a density matrix is a self adjoint (or Hermitian) positive semidefinite matrix (possibly infinite dimensional) of trace one, that… …
