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The Sum of the Tensor Resolution Becoming the Vector's Product and Its Meaning

Han Feng

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Abstract

Proves that in n-dimensional space,any q order tensor(q1) may be written as the sum of n~(q-1) tensors,among which every tensor is composed of q vector product.Generally speaking,n~(q-1) is the smallest number of the item that can be decomposed from the tensor. This decomposition may give another definition of high order tensor's covariant derivative.

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What this paper is about

Proves that in n-dimensional space,any q order tensor(q1) may be written as the sum of n~(q-1) tensors,among which every tensor is composed of q vector product.Generally speaking,n~(q-1) is the smallest number of the item that can be decomposed from the tensor. This decomposition may give another definition of high order tensor's covariant derivative.

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Available abstract

Proves that in n-dimensional space,any q order tensor(q1) may be written as the sum of n~(q-1) tensors,among which every tensor is composed of q vector product.Generally speaking,n~(q-1) is the smallest number of the item that can be decomposed from the tensor. This decomposition may give another definition of high order tensor's covariant derivative.

Key concepts: Tensor product of Hilbert spaces, Tensor contraction, Tensor (intrinsic definition), Tensor density, Tensor product, Mathematics, Cartesian tensor, Tensor product of modules

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