On the Ranks and Border Ranks of Symmetric Tensors |
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Authors: | J M Landsberg Zach Teitler |
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Institution: | 1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA
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Abstract: | 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. |
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Keywords: | |
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