Symmetric Tensor
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Beschrijving
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a symmetric tensor is tensor that is invariant under a permutation of its vector arguments. The space of symmetric tensors of rank r on a finite dimensional vector space is naturally isomorphic to the dual of the space homogeneous polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is that of the antisymmetric tensor or alternating form. Symmetric tensors occur widely in engineering, physics and mathematics.
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a symmetric tensor is tensor that is invariant under a permutation of its vector arguments. The space of symmetric tensors of rank r on a finite dimensional vector space is naturally isomorphic to the dual of the space homogeneous polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is that of the antisymmetric tensor or alternating form. Symmetric tensors occur widely in engineering, physics and mathematics.
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