Vector Spaces

Some articles on vector spaces, vector space, vectors, spaces, space:

... Supermodules over a commutative superalgebra can be viewed as generalizations of super vector spaces over a (purely even) field K ... more prominent role in super linear algebra than do super vector spaces ... so one moves from fields to commutative superalgebras and from vector spaces to modules ...
Basis (universal Algebra) - Examples - Vector Space Algebras
... In the universal algebra corresponding to a vector space with positive dimension the bases essentially are the ordered bases of this vector space ... When the vector space is finite-dimensional, for instance with, the functions in the set L of the outer condition exactly are the ones that provide the spanning and linear ... is a mere instance of present independence, which becomes equivalent to it in such vector spaces ...
Super Linear Algebra - Scope of Study - Vector Spaces
... The main structures of linear algebra are vector spaces ... A vector space over a field F is a set V together with two binary operations ... Elements of V are called vectors and elements of F are called scalars ...
Latent Semantic Indexing - Querying and Augmenting LSI Vector Spaces
... The computed Tk and Dk matrices define the term and document vector spaces, which with the computed singular values, Sk, embody the conceptual information derived from the document collection ... The similarity of terms or documents within these spaces is a factor of how close they are to each other in these spaces, typically computed as a function of the angle between the corresponding vectors ... The same steps are used to locate the vectors representing the text of queries and new documents within the document space of an existing LSI index ...
Reductive Dual Pair - Structure Theory and Classification
... Thus W is a symplectic vector space over F ... If W1 and W2 are two symplectic vector spaces and (G1, G′1), (G2, G′2) are two reductive dual pairs in the corresponding symplectic groups, then we may form a new symplectic ... Let U and V be two vector spaces over F, X = U ⊗F V be their tensor product, and Y = HomF(X, F) its dual ...

Famous quotes containing the word spaces:

    through the spaces of the dark
    Midnight shakes the memory
    As a madman shakes a dead geranium.
    —T.S. (Thomas Stearns)