Border rank of a p×q×2 tensor and the optimal approximation of a pair of bilinear forms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)


The border rank tB over the field F of the non degenerate p×q×2 tensor A = [B,C] is such that max (p,q) ≤ tB ≤ max (p,q) + S, with S=0 if the invariant polynomials of B+ λC have roots in the closure of F, s=1 otherwise. A pair of non degenerate p×q bilinear forms can be approximated with at most max(p×q)+1 non scalar multiplications over any field.


Bilinear Form Companion Matrix Approximate Algorithm Toeplitz Matrice Invariant Polynomial 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • D. Bini
    • 1
  1. 1.Istituto Matematico dell'Università di PisaItaly

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