In mathematics, specifically linear algebra and geometry, relative dimension is the dual notion to codimension. In linear algebra, given a quotient map, the difference dim V ¿ dim Q is the relative dimension; this equals the dimension of the kernel. In fiber bundles, the relative dimension of the map is the dimension of the fiber. More abstractly, the codimension of a map is the dimension of the cokernel, while the relative dimension of a map is the dimension of the kernel.
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Qubit
In quantum computing, a qubit or quantum bit is a unit of quantum information¿the quantum analogue of the classical bit. A qubit is a two-state quantum-mechanical system such as the polarization of a single photon: here the two states are vertical polarization and horizontal polarization.
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Probability theory
Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion.
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Intersection (set theory)
In mathematics, the intersection (denoted as ¿) of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. For explanation of the symbols used in this article, refer to the table of mathematical symbols.
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Quantum entanglement
Quantum entanglement occurs when particles such as photons, electrons, molecules as large as buckyballs, and even small diamonds interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description, which is indefinite in terms of important factors such as position, momentum, spin, polarization, etc.
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Linear subspace
The concept of a linear subspace (or vector subspace) is important in linear algebra and related fields of mathematics. A linear subspace is usually called simply a subspace when the context serves to distinguish it from other kinds of subspaces.
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Vector space
A vector space is a mathematical structure formed by a collection of elements called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars in this context. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below.
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Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size, deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria, finding "largest", "smallest", or "optimal" objects, and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems.
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