2025-06-11 at

Tensor Rank = Quantity Dimensions + 1

 TIL terminology : the indexing of dimensions and tensors, is different.

  • A dimension is a measurable difference / displacement.
  • But a tensor is a higher-order categorisation of differences / displacements.

So 

  • a scalar is 1-dimensional, a 1-(tuple|space), but is a 0-rank tensor, because each point has 0 dimensions of internal (mapping|relationship).
  • A vector is 2-dimensional, a 2-(tuple|space), but is a 1-rank tensor, because each point has 1 dimension of internal (mapping|relationship).

Ya? 


MathWorld : ""An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules....Tensors are generalizations of scalars (that have no indices), vectors (that have exactly one index), and matrices (that have exactly two indices) to an arbitrary number of indices."" - via Reddit

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