algebra of infinite rank

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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

• 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

• Infinite product — In mathematics, for a sequence of numbers a 1, a 2, a 3, ... the infinite product :prod {n=1}^{infty} a n = a 1 ; a 2 ; a 3 cdotsis defined to be the limit of the partial products a 1 a 2... a n as n increases without bound. The product is said… …   Wikipedia

• Von Neumann algebra — In mathematics, a von Neumann algebra or W* algebra is a * algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann,… …   Wikipedia

• Kac–Moody algebra — In mathematics, a Kac–Moody algebra is a Lie algebra, usually infinite dimensional, that can be defined by generators and relations through a generalized Cartan matrix. Kac–Moody algebras are named after Victor Kac and Robert Moody, who… …   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

• Cuntz algebra — In C* algebras, the Cuntz algebra (after Joachim Cuntz) is the universal C* algebra generated by n isometries satisfying certain relations. It is the first concrete example of a separable infinite simple C* algebra. Every simple infinite C*… …   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

• 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

• 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

• Basis (linear algebra) — Basis vector redirects here. For basis vector in the context of crystals, see crystal structure. For a more general concept in physics, see frame of reference. In linear algebra, a basis is a set of linearly independent vectors that, in a linear… …   Wikipedia