## Abstract

Vector spaces of pairs of rational vector valued functions, which are (1) invariant under the generalized backward shift and (2) endowed with a sesquilinear form which is subject to a structural identity, are studied. It is shown that any matrix can be viewed as the "Gram" matrix of a suitably defined basis for such a space. This identification is used to show that a rule due to Iohvidov for evaluating the rank of certain subblocks of a Toeplitz (or Hankel) matrix is applicable to a wider class of matrices with (appropriately defined) displacement rank equal to two. Enroute, a theory of reproducing kernel spaces is developed for nondegenerate spaces of the type mentioned above.

Original language | English |
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Pages (from-to) | 413-451 |

Number of pages | 39 |

Journal | Linear Algebra and Its Applications |

Volume | 137-138 |

Issue number | C |

DOIs | |

State | Published - 1 Jan 1990 |

Externally published | Yes |

## ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics