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A collection B of subsets of a set X forming a topological basis.

Given a matrix A, a Jordan basis satisfies Ab_(i,1)=lambda_ib_(i,1) and Ab_(i,j)=lambda_ib_(i,j)+b_(i,j-1), and provides the means by which any complex matrix A can be ...

A Schauder basis for a Banach space X is a sequence {x_n} in X with the property that every x in X has a unique representation of the form x=sum_(n=1)^(infty)alpha_nx_n for ...

A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...

A basis of a modular system M is any set of polynomials B_1, B_2, ... of M such that every polynomial of M is expressible in the form R_1B_1+R_2B_2+..., where R_1, R_2, ... ...

If R is a Noetherian ring, then S=R[X] is also a Noetherian ring.

A generalization of the Kronecker decomposition theorem which states that every finitely generated Abelian group is isomorphic to the group direct sum of a finite number of ...

A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

An ordered vector basisv_1,...,v_n for a finite-dimensional vector space V defines an orientation. Another basis w_i=Av_i gives the same orientation if the matrix A has a ...

An orientation on an n-dimensional manifold is given by a nowhere vanishing differential n-form. Alternatively, it is an bundle orientation for the tangent bundle. If an ...