I am investigating the properties underlying linear transformations between arbitrarily valued tensors.
I wish to prove or disprove this theorem:
Between any two sets of tensors A and B there exists a mapping tensor M such that M(A[N]) = B[N] where N is the index in the tensor sets.
For example:
A = [[2], [3]] B = [[10,6], [15, 9]]
then
M = [[5, 3]]
I am trying to determine that if I were to generate a randomly initialized set of tensors A and a randomly initialized set of tensors B that I could derive some single mapping tensor M that maps all the elements of A onto B. The dimensions of M are also arbitrary.
Is this possible? Are there any numerical gotchas that would get in the way?