dual basis meaning in Hindi

Examples

1. For the basis of vector fields define the dual basis to be the linear functionals such that
2. (where are the components of in a particular basis and are the components of in the corresponding dual basis ).
3. Further, for topological vector spaces, a continuous dual space can be defined, in which case a dual basis may exist.
4. Explicitly, given a Lagrangian subspace ( as defined below ), then a choice of basis defines a dual basis for a complement, by.
5. 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.
6. 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.
7. 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.
8. 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 ).
9. 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 ).
10. 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.