Examples of 'finite-dimensional' in a sentence
Meaning of "finite-dimensional"
Finite-dimensional: Used in mathematics to describe a vector space that has a finite basis
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- (of a vector space) having a basis consisting of a finite number of elements.
How to use "finite-dimensional" in a sentence
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finite-dimensional
Any finite-dimensional vertex algebra is commutative.
Not all elements need to be finite-dimensional.
This finite-dimensional problem is then implemented on a computer.
In most cases they are not finite-dimensional.
These are finite-dimensional moduli spaces.
The first part is dedicated to transformations of finite-dimensional algebras.
All norms on a finite-dimensional vector space are equivalent.
The statement is essentially the same as the finite-dimensional version.
Every finite-dimensional vector space has a basis.
Any linear operator defined on a finite-dimensional normed space is bounded.
As in the finite-dimensional case, observability is the dual notion of controllability.
Parabolic partial differential equations may have finite-dimensional attractors.
It has no finite-dimensional representations.
Then we have the following result about finite-dimensional representations.
Finite-dimensional numerical techniques were used to approximate the solution.
See also
Every linear function on a finite-dimensional space is continuous.
Additional algebraic structures can also be imposed in the finite-dimensional case.
Every linear operator on a finite-dimensional space is trivially locally finite.
In finite-dimensional case linear operators can be represented by matrices in the following way.
Accordingly, every invertible linear transformation of a finite-dimensional linear topological space is a homeomorphism.
In the finite-dimensional case, the second condition above is implied by the first.
He introduced the Gelfand-Tsetlin basis for finite-dimensional representations of classical groups.
On a finite-dimensional vector space this topology is the same for all norms.
A statistical model is semiparametric if it has both finite-dimensional and infinite-dimensional parameters.
Infinite-dimensional optimization problems can be more challenging than finite-dimensional ones.
The spectrum of an operator on a finite-dimensional vector space is precisely the set of eigenvalues.
Kadets also made several contributions to the theory of finite-dimensional normed spaces.
Hilbert spaces generalize finite-dimensional vector spaces to countably-infinite dimensions.
For simplicity, it will be assumed that all objects in the article are finite-dimensional.
One distinguishes between finite-dimensional representations and infinite-dimensional ones.
Minkowski proved that symmetric convex bodies induce norms in finite-dimensional vector spaces.
This fact characterizes finite-dimensional vector spaces without referring to a basis.
I will survey classical theory and talk about recent work on its finite-dimensional counterparts.
For operators on a finite-dimensional vector space, local nilpotence is equivalent to nilpotence.
Partial differential equations are solved by first discretizing the equation, bringing it into a finite-dimensional subspace.
If the vector space is a finite-dimensional real or complex one, all norms are equivalent.
The second step is the discretization, where the weak form is discretized in a finite-dimensional space.
Natural isomorphism between a finite-dimensional vector space and its second dual.
Finite-dimensional associative division algebras over the real numbers are very rare.
First, we classify all irreducible finite-dimensional representations of an equivariant map queer lie superalgebra.
A Hausdorff topological vector space is locally compact if and only if it is finite-dimensional.
This means that every finite-dimensional representation decomposes as a direct sum of irreducible representations.
There is in general no natural isomorphism between a finite-dimensional vector space and its dual space.
If two finite-dimensional irreducible representations have the same highest weight, they are isomorphic.
The most important distinction is between finite-dimensional representations and infinite-dimensional ones.
The finite-dimensional alternative division algebras over the field of real numbers have been classified.
This concept can be generalized to any finite-dimensional vector space over any field.
The finite-dimensional division algebras over the field of real numbers can be classified nicely.
The most difficult part is the last one ; the construction of a finite-dimensional irreducible representation.
All finite-dimensional vector spaces are nuclear because every operator on a finite-dimensional vector space is nuclear.
