With the pointwise addition and scalar multiplication of sections, " F " ( " U " ) becomes itself a real vector space.
22.
The tangent space and the cotangent space at a point are both real vector spaces of the same dimension and therefore isomorphic to each other via many possible isomorphisms.
23.
With the latter definition, convex hulls may be extended from Euclidean spaces to arbitrary real vector spaces; they may also be generalized further, to oriented matroids.
24.
Thus, the set of all possible physical states is the two-dimensional real vector space with a-axis and a-axis called the phase space.
25.
To get a more visual flavour of singular values and SVD factorization at least when working on real vector spaces consider the sphere of radius one in.
26.
The set of local vector fields on " M " forms a structure known as a sheaf of real vector spaces on " M ".
27.
Moreover every irreducible representation on a complex vector space can be constructed from a unique irreducible representation on a real vector space in one of the three ways above.
28.
The space \ mathcal D _ m ( M ) of " m "-dimensional currents on M is a real vector space with operations defined by
29.
For certain linear operators there is no " non-trivial " invariant subspace; consider for instance a rotation of a two-dimensional real vector space.
30.
In some sense, these operators play the role of the real numbers ( being equal to their own " complex conjugate " ) and form a real vector space.
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