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rank of algebra

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  • Rank (linear algebra) — The column rank of a matrix A is the maximum number of linearly independent column vectors of A. The row rank of a matrix A is the maximum number of linearly independent row vectors of A. Equivalently, the column rank of A is the dimension of the …   Wikipedia

  • Nonnegative rank (linear algebra) — In linear algebra, the nonnegative rank of a nonnegative matrix is a concept similar to the usual linear rank of a real matrix, but adding the requirement that certain coefficients and entries of vectors/matrices have to be nonnegative. For… …   Wikipedia

  • Rank — is a very broad term with several meanings. As a noun it is usually related to a relative position or to some kind of ordering (see also ranking). As an adjective it is used to mean profuse, conspicuous, absolute, or unpleasant, especially in… …   Wikipedia

  • Rank (mathematics) — Rank means a wide variety of things in mathematics, including: * Rank (linear algebra) * Rank of a tensor * Rank of an abelian group * Rank of a Lie group * Percentile rank * Rank (differential topology) * Rank of a vector bundle * Rank (set… …   Wikipedia

  • Rank (computer programming) — In computer programming, rank with no further specifications is usually a synonym for (or refers to) number of dimensions ; thus, for instance, a bi dimensional array has rank two , a three dimensional array has rank three and so on.Strictly, no… …   Wikipedia

  • Rank–nullity theorem — In mathematics, the rank–nullity theorem of linear algebra, in its simplest form, states that the rank and the nullity of a matrix add up to the number of columns of the matrix. Specifically, if A is an m by n matrix over the field F , then :rank …   Wikipedia

  • Exterior algebra — In mathematics, the exterior product or wedge product of vectors is an algebraic construction generalizing certain features of the cross product to higher dimensions. Like the cross product, and the scalar triple product, the exterior product of… …   Wikipedia

  • Nichols algebra — The Nichols algebra of a braided vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted by and named after the mathematician Warren Nichols. It takes the role of quantum Borel part of a pointed …   Wikipedia

  • Cluster algebra — Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky (2002, 2003, 2007). A cluster algebra of rank n is an integral domain A, together with some subsets of size n called clusters whose union generates the… …   Wikipedia

  • Finite rank operator — In functional analysis, a finite rank operator is a bounded linear operator between Banach spaces whose range is finite dimensional. Finite rank operators on a Hilbert space A canonical form Finite rank operators are matrices (of finite size)… …   Wikipedia

  • Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… …   Wikipedia

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