basis element sentence in Hindi
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- Here | v \ rangle is the standard basis element of \ mathbf { R } ^ n with a one in the v ^ { th } position.
- Often the basis elements " Q " come in complex conjugate pairs, so the real subspace can be recovered as the fixed points of complex conjugation.
- Insofar as \ mathfrak { g } is just an ordinary vector space, the generators of \ mathfrak { g } correspond to basis elements of the vector space.
- In contrast, non-zero free abelian groups are never divisible, because it is impossible for any of their basis elements to be nontrivial integer multiples of other elements.
- Green's functions can be expanded in terms of the basis elements ( harmonic functions ) which are determined using the separable coordinate systems for the linear partial differential equation.
- From the PBW theorem, it is clear that all such central elements will be linear combinations of symmetric homogenous polynomials in the basis elements e _ a of the Lie algebra.
- For each value of " k " there are " n " choose " k " basis elements, so the total dimension of the Clifford algebra is
- But in 3D, with three vector directions, there are three bivector basis elements ? 1 ? 2, ? 2 ? 3, ? 3 ? 1, so three imaginaries.
- You can send the basis elements to their new spots with reflections one at a time and show that the later reflections don't mess with the basis elements that were already set.
- You can send the basis elements to their new spots with reflections one at a time and show that the later reflections don't mess with the basis elements that were already set.
- A closer inspection of the convolution of two basis elements as shown in the equation above reveals that the multiplication in L ^ 1 ( G ) corresponds to that in \ C [ G ].
- Terms appear in the expansion of the transition probability above which involve i \ ne j; these can be thought of as representing " interference " between the different basis elements or quantum alternatives.
- The relation to complex numbers becomes clearer, too : in 2D, with two vector directions ? 1 and ? 2, there is only one bivector basis element ? 1 ? 2, so only one imaginary.
- It is easy to check that f is a solution to Cauchy's functional equation given a definition of f on the basis elements, f : \ mathcal { B } \ rightarrow \ mathbb { R }.
- This is the defining condition for a generating set of a Clifford algebra . ? } } } of a ( ? ?) representation of .-- > Further basis elements of the Clifford algebra are given by
- We have a base B at \ theta for a translation invariant topology, so the set of all basis elements for the whole set are of the form x + B . In this specific part, we are trying to show
- If the answer is yes, then the next question is to find a minimal basis, and ask whether the module of polynomial relations between the basis elements ( known as the syzygies ) is finitely generated over k [ V ].
- The problem can also be studied from the abstract point of view : every Hilbert space has an orthonormal basis, and every element of the Hilbert space can be written in a unique way as a sum of multiples of these basis elements.
- An " evolution algebra " over a field is an algebra with a basis on which multiplication is defined by the product of distinct basis terms being zero and the square of each basis element being a linear form in basis elements.
- An " evolution algebra " over a field is an algebra with a basis on which multiplication is defined by the product of distinct basis terms being zero and the square of each basis element being a linear form in basis elements.
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