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Matrix subspaces and determinantal hypersurfaces

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Arkiv för Matematik

Abstract

Nonsingular matrix subspaces can be separated into two categories: by being either invertible, or merely possessing invertible elements. The former class was introduced for factoring matrices into the product of two matrices. With the latter, the problem of characterizing the inverses and related nonlinear matrix geometries arises. For the singular elements there is a natural concept of spectrum defined in terms of determinantal hypersurfaces, linking matrix analysis with algebraic geometry. With this, matrix subspaces and the respective Grassmannians are split into equivalence classes. Conditioning of matrix subspaces is addressed.

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Authors and Affiliations

  1. Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FI-02015, Helsinki University of Technology, Finland

    Marko Huhtanen

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  1. Marko Huhtanen
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Correspondence to Marko Huhtanen.

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Supported by the Academy of Finland.

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Huhtanen, M. Matrix subspaces and determinantal hypersurfaces. Ark Mat 48, 57–77 (2010). https://doi.org/10.1007/s11512-009-0098-0

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  • DOI: https://doi.org/10.1007/s11512-009-0098-0

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