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mikeeey
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Can some one write for me the Symmetric part of a third order tensor (as a tensor form)
Thanks .
Thanks .
A 3rd order tensor is a mathematical object that describes the relationship between three sets of vectors or scalars. It is represented by a set of numbers arranged in a specific way, similar to a matrix.
The symmetric part of a tensor is the part of the tensor that remains unchanged when the order of the indices is reversed. In other words, the symmetric part is invariant under the interchange of indices.
To write the symmetric part of a 3rd order tensor in tensor form, you can use the symmetrization operator. This operator is represented by a square bracket with a subscript indicating the order of symmetry. For a 3rd order tensor, the symmetrization operator is [3].
Expressing the symmetric part of a tensor in tensor form allows for easier manipulation and calculation of tensor operations. It also helps to identify and understand the symmetry properties of a tensor, which can be useful in various applications, such as mechanics and physics.
No, the symmetric part of a 3rd order tensor cannot be written in matrix form because it has more than two indices. Matrices can only represent tensors with two indices. However, the symmetric part of a 3rd order tensor can be written in a reduced form using the Kronecker delta symbol and the Levi-Civita symbol.