Decomposition of tensors
Provides a foundational theoretical result for tensor decomposition, addressing a long-standing conjecture in multilinear algebra.
The paper proves a unique finite strongly orthogonal decomposition for tensors, which determines the exact number of critical points of a multilinear form, resolving a finiteness conjecture by Friedland.
We consider representations of tensors as sums of decomposable tensors or, equivalently, decomposition of multilinear forms into one--forms. In this short note we show that there exists a particular finite strongly orthogonal decomposition which is essentially unique and yields all critical points of the multilinear form on the torus. In particular, this determines exactly the number of critical points of the multilinear form, giving an affirmative answer to a finiteness conjecture by Friedland.