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dasarpmar / lowerbounds-survey

A survey of known lower bounds in arithmetic circuits.
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Tensor rank of V ⊗ W #11

Closed dasarpmar closed 7 years ago

dasarpmar commented 8 years ago

I thought that if V and W are tensors of rank r and s respectively, then V ⊗ W has tensor-rank rs. Is this true at all? (Of course rs is an upper bound but is it tight?)

dasarpmar commented 7 years ago

It is not tight. All the matrix multiplication algorithms are counterexamples.