evaluation map sentence in Hindi
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- In this case, the evaluation map will be an embedding.
- It is the coarsest topology on for which all evaluation maps, are continuous.
- Then the image of the evaluation map forms a pseudocycle, which induces a well-defined homology class of the expected dimension.
- The homology class defined by the evaluation map is independent of the choice of generic \ omega-tame J and perturbation \ nu.
- More precisely, a topological vector space X is called "'stereotype "'if the evaluation map into the "'stereotype second dual space "'
- If, however, we choose a nice infinite field then we can conclude that two polynomials are equal iff their evaluation maps are equal, and these " can " be composed.
- Equivalently, it is the coarsest topology such that the evaluation maps T \ mapsto Tx ( taking values in " H " ) are continuous for each fixed " x " in " H ".
- In terms of the diagonal map which induces the map \ Delta _ * on the chain complex, and \ varepsilon \ colon C _ p ( X ) \ otimes C ^ q ( X ) \ to \ mathbb { Z } is the evaluation map ( always 0 except for p = q ).
- One can work around this difficulty in the particular situation at hand, since the above right-evaluation map does become a ring homomorphism if the matrix is in the center of the ring of coefficients, so that it commutes with all the coefficients of the polynomials ( the argument proving this is straightforward, exactly because commuting with coefficients is now justified after evaluation ).
- More abstractly, the outer product is the bilinear map W \ times V ^ * \ to \ operatorname { Hom } ( V, W ) sending a vector and a covector to a rank 1 linear transformation ( simple tensor of type ( 1, 1 ) ), while the inner product is the bilinear evaluation map V ^ * \ times V \ to F given by evaluating a covector on a vector; the order of the domain vector spaces here reflects the covector / vector distinction.
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