Where the semicolon represents a covariant derivative, and the brackets denote anti-symmetrization.
2.
This process is known as symmetrization.
3.
This identity is equivalent the following classical relations, the first of which is the symmetrization relation of Plemelj:
4.
Then define the word metric with respect to S to be the word metric with respect to the symmetrization of S.
5.
After an application of Jensen's inequality different signs could be introduced ( hence the name symmetrization ) without changing the expectation.
6.
Where C _ { abcd } is the Weyl tensor, the semicolon denotes the covariant derivative, and the subscripted parentheses indicate symmetrization.
7.
However, the tensor T is not yet totall anti-symmetric, in fact the anti-symmetrization will lead to the Nijenhuis tensor.
8.
The proof of the ( first part of ) VC inequality, relies on symmetrization, and then argue conditionally on the data using concentration inequalities ( in particular Hoeffding's inequality ).
9.
When symmetrization or anti-symmetrization is unnecessary, " N "-particle spaces of states can be obtained simply by tensor products of one-particle spaces, to which we will return later.
10.
When symmetrization or anti-symmetrization is unnecessary, " N "-particle spaces of states can be obtained simply by tensor products of one-particle spaces, to which we will return later.
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