How to define a tensor
Aleksandar Bakša
Abstract
Aleksandar Bakša
Abstract
This work proposes a way to define tensors, which is naturally imposed by the application of tensor calculation in mechanics. Taking as the staring point the problem of determining voltage, the voltage tensor is defined as a linear operator that transforms the covariant vector into a contravariant vector. The general type tensor is defined as the element of the tensor space - linear space, in which the tensor product is defined. From this definition it is possible to deduce the transformation method for tensor coordinates.
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This work proposes a way to define tensors, which is naturally imposed by the application of tensor calculation in mechanics. Taking as the staring point the problem of determining voltage, the voltage tensor is defined as a linear operator that transforms the covariant vector into a contravariant vector. The general type tensor is defined as the element of the tensor space - linear space, in which the tensor product is defined. From this definition it is possible to deduce the transformation method for tensor coordinates.
Key concepts: Tensor contraction, Tensor product of Hilbert spaces, Cartesian tensor, Tensor density, Covariance and contravariance of vectors, Tensor field, Tensor (intrinsic definition), Symmetric tensor