Examples of using Vector spaces in English and their translations into Dutch
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From real to complex vector spaces and back.
The solutions of homogeneous linear differential equations form vector spaces.
There are many textbooks on vector spaces and linear algebra.
Complex vector spaces.
The sum of the vector spaces M and N,
Further abstract algebraic concepts such as modules, vector spaces and algebras also form groups.
Moreover, two vector spaces over the same field F are isomorphic if
associative algebras(rings that are also vector spaces) are often studied via their categories of modules.
Unlike vector spaces, not all abelian groups have a basis,
It should be remarked that on generic complex vector spaces there is no canonical notion of complex conjugation.
modules, vector spaces, and algebras.
His doctoral thesis"Rational Vector Spaces" was supervised by Cornelius Joseph Everett,
In mathematics, Functional analysis is concerned with the study of vector spaces and operators acting upon them.
As such they are topological vector spaces, in which topological notions like the openness
while LF-spaces are complete uniform vector spaces arising as limits of Fréchet spaces. .
Any element in the direct sum of two vector spaces of matrices can be represented as a direct sum of two matrices.
Representation theory is a branch of mathematics that studies abstract algebraic structures by"representing" their elements as linear transformations of vector spaces.
Note that any element in the direct sum of two vector spaces of matrices could be represented as a direct sum of two matrices.
Since vector spaces over K(as a field)
rings, vector spaces, modules, Lie algebras,
Vector spaces whose elements are"smooth" in some sense tend to be nuclear spaces; a typical example
The category K-Vect(some authors use VectK) has all vector spaces over a fixed field K as objects
also arise in the study of spatial symmetries and symmetries of vector spaces in general, as well as the study of polynomials.
Infinite-dimensional vector spaces arise naturally in mathematical analysis,
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
The reason for working with arbitrary vector spaces instead of Rn is that it is often preferable to work in a coordinate-free manner that is,
the representations as functors from the object category to the category of vector spaces.
These vector spaces are generally endowed with additional structure, which may be a topology,
act on vector spaces.
Vector spaces are the subject of linear algebra and are well understood from this point of view since vector spaces are characterized by their dimension,