irreducible mapping
11Eigenvalues 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… …
12Coherent 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 …
13Gelfand-Naimark-Segal construction — In functional analysis, given a C* algebra A , the Gelfand Naimark Segal construction establishes a correspondence between cyclic * representations of A and certain linear functionals on A (called states ). The correspondence is shown by an… …
14Separable polynomial — In mathematics, two slightly different notions of separable polynomial are used, by different authors. According to the most common one, a polynomial P(X) over a given field K is separable if all its roots are distinct in an algebraic closure of… …
15Decoherence-free subspaces — A decoherence free subspace (DFS) is a subspace of a system s Hilbert space that is invariant to non unitary dynamics. Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the environment… …
16Spinor — In mathematics and physics, in particular in the theory of the orthogonal groups (such as the rotation or the Lorentz groups), spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the… …
17Markov chain — A simple two state Markov chain. A Markov chain, named for Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized …
18Quantum group — In mathematics and theoretical physics, quantum groups are certain noncommutative algebras that first appeared in the theory of quantum integrable systems, and which were then formalized by Vladimir Drinfel d and Michio Jimbo. There is no single …
19Allen Hatcher — Allen Edward Hatcher is an American topologist and also a noted author. His book Algebraic Topology , which is the first in a series, is considered by many to be one of the best introductions to the subject.He received his Ph.D. under the… …
20Specified complexity — Part of a series of articles on Intelligent design …
