Tensor ranks for the inversion of tensor-product binomials

Tensor ranks for the inversion of tensor-product binomials

The main result reads: if a nonsingular matrix A of order n = p q 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 .

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Veröffentlicht in:Journal of computational and applied mathematics 2010-10, Vol.234 (11), p.3170-3174
1. Verfasser: Tyrtyshnikov, Eugene
Format: Artikel
Sprache:eng
Schlagworte:
Binomials
Computation
Estimates
Inverse matrices
Inversions
Kronecker product
Low-rank matrices
Mathematical analysis
Mathematical models
Multilevel matrices
Tensor ranks
Tensors
Toeplitz matrices
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Zusammenfassung:The main result reads: if a nonsingular matrix A of order n = p q 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 .
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2010.02.006