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Results tagged with multilinear-algebra
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user 88133
Tensors, multivectors, wedge products, multilinear maps, exterior (Grassmann) algebras.
7
votes
Accepted
Is the Waring rank homogeneous polynomials sub-multiplicative?
You asked:
Is $W(P \otimes Q) \leq W(P) W(Q)$ for two homogeneous polynomials $P$ and $Q$?
First, I think you have to be a little bit careful about the difference between tensor product and mult …
- 6,237
7
votes
Accepted
Waring rank of monomials, and how it depends on the ground field
The answer to question 1 is affirmative. There are several lower bounds in various papers. I'll take the idea from https://arxiv.org/abs/1503.08253 (Buczyński and myself, "Some examples of forms of hi …
- 6,237
7
votes
Tensor rank of anti-symmetric tensor
The tensor ranks of determinants and permanents are currently not known. In the $3 \times 3$ case it is known: the $3 \times 3$ determinant has tensor rank $5$ and the $3 \times 3$ permanent has tenso …
- 6,237