On the Ranks and Border Ranks of Symmetric Tensors Academic Article uri icon


  • Motivated by questions arising in signal processing, computational complexity, and other areas, we study the ranks and border ranks of symmetric tensors using geometric methods. We provide improved lower bounds for the rank of a symmetric tensor (i.e., a homogeneous polynomial) obtained by considering the singularities of the hypersurface defined by the polynomial. We obtain normal forms for polynomials of border rank up to five, and compute or bound the ranks of several classes of polynomials, including monomials, the determinant, and the permanent. © 2009 SFoCM.

author list (cited authors)

  • Landsberg, J. M., & Teitler, Z.

citation count

  • 92

publication date

  • October 2009