Examples of 'finite-dimensional vector' in a sentence
Meaning of "finite-dimensional vector"
finite-dimensional vector: a mathematical concept representing a quantity with both direction and magnitude in a space with a limited number of dimensions
How to use "finite-dimensional vector" in a sentence
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finite-dimensional vector
All norms on a finite-dimensional vector space are equivalent.
Minkowski proved that symmetric convex bodies induce norms in finite-dimensional vector spaces.
Every finite-dimensional vector space has a basis.
This concept can be generalized to any finite-dimensional vector space over any field.
On a finite-dimensional vector space this topology is the same for all norms.
Natural isomorphism between a finite-dimensional vector space and its second dual.
All finite-dimensional vector spaces are nuclear because every operator on a finite-dimensional vector space is nuclear.
There is in general no natural isomorphism between a finite-dimensional vector space and its dual space.
For operators on a finite-dimensional vector space, local nilpotence is equivalent to nilpotence.
Ado's theorem states that every finite-dimensional Lie algebra has a faithful representation on a finite-dimensional vector space.
Hilbert spaces generalize finite-dimensional vector spaces to countably-infinite dimensions.
Finite-dimensional vector spaces, there exists a finite basis.
The spectrum of an operator on a finite-dimensional vector space is precisely the set of eigenvalues.
Finite-dimensional vector spaces are better-behaved than infinite-dimensional ones.
The rank-nullity theorem for finite-dimensional vector spaces is equivalent to the statement.
See also
Finite-dimensional vector spaces, there exists a finite basis of M. Example, Rn.
Every linear transformation between finite-dimensional vector spaces arises in this fashion ; see the following section.
Linear functional " is rarely used for finite-dimensional vector spaces.
Let V be a finite-dimensional vector space over a field k.
Is an exact sequence of finite-dimensional vector spaces, then.
For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication,.
H3, The tangent space of F is a finite-dimensional vector space over k.
Given any finite-dimensional vector space, an orthonormal basis could be found by the Gram-Schmidt procedure.
Like any linear transformation of finite-dimensional vector spaces, a rotation can always be represented by a matrix.
Let V be a finite-dimensional vector space over a field k and f, V → V { \ displaystyle f, V \ to V } a linear map with minimal polynomial q.
For some V, namely precisely the finite-dimensional vector spaces, this map is an isomorphism.
The converse is true for finite-dimensional vector spaces, but not for infinite-dimensional vector spaces.
This fact characterizes finite-dimensional vector spaces without referring to a basis.
Let V be a finite-dimensional vector space.
Any subspace of a finite-dimensional vector space is finite-dimensional.
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