8 research outputs found
Concise tensors of minimal border rank
We determine defining equations for the set of concise tensors of minimal
border rank in when and the set of concise
minimal border rank -generic tensors when . We solve this classical
problem in algebraic complexity theory with the aid of two recent developments:
the 111-equations defined by Buczy\'{n}ska-Buczy\'{n}ski and results of
Jelisiejew-\v{S}ivic on the variety of commuting matrices. We introduce a new
algebraic invariant of a concise tensor, its 111-algebra, and exploit it to
give a strengthening of Friedland's normal form for -degenerate tensors
satisfying Strassen's equations. We use the 111-algebra to characterize wild
minimal border rank tensors and classify them in .Comment: v2, fina