# What are vector spaces?

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

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 ...
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 vector space W ... 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 ...
Basis (universal Algebra) - Examples - Vector Space Algebras
... 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 independence ... which becomes equivalent to it in such vector spaces ... square arrays of field numbers (namely, usual vector-space square matrices) that serve to build the endomorphisms of vector spaces (namely, linear maps into themselves) ...
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 ... 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 ... 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 ...
Supermodule
... be viewed as generalizations of super vector spaces over a (purely even) field K ... often play a more prominent role in super linear algebra than do super vector spaces ... In doing so one moves from fields to commutative superalgebras and from vector spaces to modules ...

### Famous quotes containing the word spaces:

Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.
Blaise Pascal (1623–1662)