- #1
George Keeling
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- Is it necessary to have two numbers to specify the rank of a tensor?
When I started learning about tensors the tensor rank was drilled into me. "A tensor rank ##\left(m,n\right)## has ##m## up indices and ##n## down indices." So a rank (1,1) tensor is written ##A_\nu^\mu,A_{\ \ \nu}^\mu## or is that ##A_\nu^{\ \ \ \mu}##? Tensor coefficients change when the indices move up or down but surely the tensor itself stays the same. Can I forget about the ##\left(m,n\right)## business and just need the rank of a tensor which is ##m+n## = the total number of indices?