4 ms·

crudely, linear transformations : matrices :: multilinear transformations : tensors.

• Konohamaru 6y ago
  It has to behave in a certain way to be a tensor.
  • deleted 6y ago
    [deleted]
  • ogogmad 6y ago
    Given a vector space V over a field F, a tensor is a multilinear map T: V x V x V x ... x V^* x V^* x V^* -> F You're mixing up geometric objects (multilinear transformations) with their coordinate representations. A geometric object, such as a multilinear map, is automatically invariant to the coordinate system. An array of numbers, like a matrix, is not.
    • Konohamaru 6y ago
      Actually you're right. I was mixing up covariant and contravariant vectors with tensors. Although tensors do decompose into covariant and contravariant components, as your definition states.