new vector spaces from old ones
This entry list methods that give new vector spaces from old ones.
Changing the field (complexification, etc.)
direct product of vectors spaces
Tensor product of vector spaces (http://planetmath.org/TensorProductClassical)
The space of linear maps from one vector space to another, also denoted by , or simply , where and are vector spaces over the field
The space of endomorphisms of a vector space. Using the notation above, this is the space
dual vector space (http://planetmath.org/DualSpace), and bi-dual vector space. Using the notation above, this is the space , or simply .
Wedge product of vector spaces
A field is a vector space over itself. Consider a set and the set of all functions from to . Then has a natural vector space structure. If is finite, then can be viewed as a vector space having as a basis.
Vector spaces involving a linear map
Suppose is a linear map.
Topological vector spaces
Spaces of structures and subspaces of the tensor algebra of a vector space
There are also certain spaces of interesting structures on a vector space that at least in the case of finite dimension correspond to certain subspaces of the tensor algebra of the vector space. These spaces include:
The space of Hermitian inner products.
the space of symplectic structures.
space of connections
|Title||new vector spaces from old ones|
|Date of creation||2013-03-22 15:31:08|
|Last modified on||2013-03-22 15:31:08|
|Last modified by||matte (1858)|