dual basis वाक्य
उदाहरण वाक्य
मोबाइल
- For the basis of vector fields define the dual basis to be the linear functionals such that
- (where are the components of in a particular basis and are the components of in the corresponding dual basis ).
- Further, for topological vector spaces, a continuous dual space can be defined, in which case a dual basis may exist.
- Explicitly, given a Lagrangian subspace ( as defined below ), then a choice of basis defines a dual basis for a complement, by.
- Using a dual basis can provide a way to easily communicate between devices that use different bases, rather than having to explicitly convert between bases using the change of bases formula.
- On the dual basis that this was 37 years ago and I am now 83 years old, I believe I can excuse myself for not recalling my score that first day.
- A basis gives such a form ( via the dual basis ), hence when working on with a Euclidean metric and a fixed orthonormal basis, one can work with only subscripts.
- Furthermore, if a dual basis is implemented then conversion from an element in the original basis to the dual basis can be accomplished with multiplication by the multiplicative identity ( usually 1 ).
- Furthermore, if a dual basis is implemented then conversion from an element in the original basis to the dual basis can be accomplished with multiplication by the multiplicative identity ( usually 1 ).
- A "'dual basis "'is not a concrete basis like the polynomial basis or the normal basis; rather it provides a way of using a second basis for computations.
- There are as many dual basis vectors \ omega ^ i as there are basis vectors \ mathbf { e } _ i, so the dual space has the same dimension as the linear space itself.
- Using an explicit basis for " V " and the corresponding dual basis for " V " ", one can show that this gives the same definition of the trace as given above.
- The association of a dual basis with a basis gives a map from the space of bases of " V " to the space of bases of " V " ", and this is also an isomorphism.
- A basis can be chosen according to such a form, and actually that's often what one does; e . g ., orthonormal basis . ( I just noticed the article doesn't even mention dual basis, which is an important concept .)
- Given a nondegenerate quadratic form on " V ", " V " " becomes naturally identified with " V ", and the dual basis may be regarded as elements of " V ", but are not in general the same set as the original basis.
- T1 follows the G3 ( MP2 ) recipe, however, by substituting an HF / 6-31G * for the MP2 / 6-31G * geometry, eliminating both the HF / 6-31G * frequency and QCISD ( T ) / 6-31G * energy and approximating the MP2 / G3MP2large energy using dual basis set RI-MP2 techniques, the T1 method reduces computation time by up to 3 orders of magnitude.
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