## Arkiv för Matematik

### Matrix subspaces and determinantal hypersurfaces

Marko Huhtanen

#### 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.

#### Note

Supported by the Academy of Finland.

#### Article information

Source
Ark. Mat., Volume 48, Number 1 (2010), 57-77.

Dates
Received: 30 April 2008
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907105

Digital Object Identifier
doi:10.1007/s11512-009-0098-0

Mathematical Reviews number (MathSciNet)
MR2594586

Zentralblatt MATH identifier
1191.15010

Rights
2009 © Institut Mittag-Leffler

#### Citation

Huhtanen, Marko. Matrix subspaces and determinantal hypersurfaces. Ark. Mat. 48 (2010), no. 1, 57--77. doi:10.1007/s11512-009-0098-0. https://projecteuclid.org/euclid.afm/1485907105

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