Arkiv för Matematik

Matrix subspaces and determinantal hypersurfaces

Marko Huhtanen

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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.


Supported by the Academy of Finland.

Article information

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

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

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

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