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of all but the highest-dimensioned vectors in (a sum of products of) which the tensor can be expressed, which is when each product is of vectors from a finite-dimensional vector space of dimension .

In indices, a tensor of rank 1 is a tensor of the form

The rank of a tensor of order 2 agrees with the rank when the tensor is regarded as a matrix, and can be determined from Gaussian elimination for instance. The rank of an order 3 or

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