Tensor ranks for the inversion of tensor-product binomials

Authors:
Eugene Tyrtyshnikov
Affiliations:
Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkin Street, 8, Moscow 119333, Russian Federation
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The main result reads: if a nonsingular matrix A of order n=pq is a tensor-product binomial with two factors then the tensor rank of A^-^1 is bounded from above by min{p,q}. The estimate is sharp, and in the worst case it amounts to n.