Hello. I keep on encountering the need to find the Tensor or Kronecker product of two vectors. Based on the definition, If I found the product of two 2D vectors, I would get a 4-dimensional vector. Some authors claim this is the correct interpretation.(adsbygoogle = window.adsbygoogle || []).push({});

However the dyadic product, which many claim is just the 1st order case of the tensor product, would generate a second-order tensor. In other words, if I multiplied my two 2D vectors, I would get a 2x2 matrix. This is essentially finding the tensor product between the first vector and thetransposeof the second vector.

This troubles me. The first interpretation is consistent with the fundamental definition of the vector product, but the latter version is necessary for things like the rotation tensor definition to be true:

[tex] R = I\cos\theta + \sin\theta[\mathbf u]_{\times} + (1-\cos\theta)\mathbf{u}\otimes\mathbf{u} [/tex]

Which version is correct, and how can it be made consistent with the other version? Thanks for any help.

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# Tensor product for vectors

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