A sampled single dimensional signal is a vector. A sampled image is a matrix. Is video considered a rank-3 tensor since it is a set of images stacked on top of each other?
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$\begingroup$ Tensor is not just a higher rank array, it must be independent of the coordinate system. In your case I'd say that a video is a rank-3 array. $\endgroup$– SturmCommented Sep 26, 2013 at 22:33
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$\begingroup$ So, by independent of coordinate system, do you mean that a tensor does not have a basis? Sorry, brand new to Tensors! $\endgroup$– user5535Commented Sep 26, 2013 at 23:00
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$\begingroup$ Tensor is used for multi-way array; not for the tensor field. So it is just a generic name for multi-way array in machine learning community (search: tensor factorization). So, from this point, yes video is a tensor, it is an array of dimension $m\times n\times 3$. $\endgroup$– DenizCommented Jan 9, 2014 at 22:11
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$\begingroup$ @Sturm I think you might be mixing up the terms "tensor" and "tensor field". I think depending on the field you are in, these are sometimes used interchangeably. $\endgroup$– valCommented Jan 9, 2014 at 23:40
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yes - a video signal would be considered 3rd order tensor.
scalars are 0-order tensors, vectors are 1st order tensors, matrices are 2nd order tensor, data volumes are 3rd order tensors and so on for multi-dimensional arrays.
