A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations
1997 (English)In: SIAM Journal on Matrix Analysis and Applications, Vol. 18, no 3, 653-692 p.Article in journal (Refereed) Published
We derive versal deformations of the Kronecker canonical form by deriving the tangent space and orthogonal bases for the normal space to the orbits of strictly equivalent matrix pencils. These deformations reveal the local perturbation theory of matrix pencils related to the Kronecker canonical form. We also obtain a new singular value bound for the distance to the orbits of less generic pencils. The concepts, results, and their derivations are mainly expressed in the language of numerical linear algebra. We conclude with experiments and applications.
Place, publisher, year, edition, pages
1997. Vol. 18, no 3, 653-692 p.
IdentifiersURN: urn:nbn:se:umu:diva-21914ISBN: 0895-4798OAI: oai:DiVA.org:umu-21914DiVA: diva2:212167
Awarded the SIAM Linear Algebra Prize 2000 for the most outstanding scientific paper in applied linear algebra published during 1997-99.2009-04-212009-04-212011-02-22