Let us choose an expansion where the resulting basis elements interact with the environment in an element-specific way.
12.
The first three relations show that products of the ( non-real ) basis elements are anti-commutative.
13.
The coefficients appearing on these basis elements are sometimes known abstractly as the Fourier coefficients of the element of the space.
14.
Instead, tensors are defined by how their coordinates and basis elements change under a transformation from one coordinate system to another.
15.
For a full description of the remaining basis elements other than and of the Clifford algebra, please see the article Dirac algebra.
16.
A component of a tensor is a real number which is used as a coefficient of a basis element for the tensor space.
17.
:For ( 2 ), if you choose an orthonormal basis, the isometries are characterized by where they send those basis elements.
18.
The Virasoro algebra also has conformal algebraic counterparts, which basically come from arranging all the basis elements into generating series and working with single objects.
19.
For example, in two dimensions there are two orthogonal basis vectors, e _ 1, e _ 2 and the associated highest-grade basis element is
20.
In the case of finite fields, this means that each of the basis elements is related to any one of them by applying the characteristic of the field.
