Examples of using Vector spaces in English and their translations into Romanian
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However, vector spaces per se do not offer a framework to deal with the question- crucial to analysis- whether a sequence of functions converges to another function.
Most notably, in functional analysis pseudometrics often come from seminorms on vector spaces, and so it is natural to call them"semimetrics".
Ordered vector spaces, for example Riesz spaces, are fundamental to Lebesgue integration, which relies on
This table shows important examples of tensors on vector spaces and tensor fields on manifolds.
Vector spaces stem from affine geometry via the introduction of coordinates in the plane
Vector spaces are the subject of linear algebra
Vector spaces may be generalized in several ways,
For example, scalar multiplication of vector spaces takes a scalar
Any bijective map between their bases can be uniquely extended to a bijective linear map between the vector spaces.
y yields an isomorphism of vector spaces.
There is also an abstract notion of conjugation for vector spaces formula_54 over the complex numbers.
Representation theory fruitfully transfers the good understanding of linear algebra and vector spaces to other mathematical domains such as group theory.
Representation theory fruitfully transfers the good understanding of linear algebra and vector spaces to other mathematical domains such as group theory.
Leon Ratovski's work on vector spaces has been deeply influential,
many codes are constructed as subspaces of vector spaces over finite fields.
A vector bundle is a family of vector spaces parametrized continuously by a topological space X.[93]
For infinite-dimensional vector spaces, inequivalent topologies lead to inequivalent notions of tensor, and these various isomorphisms may
the target category of vector spaces can be replaced by other well-understood categories.
there is, in general vector spaces, no notion of nearness, angles or distances.