Abstract
This chapter presents the general theory of block similarity for arbitrary (finite dimensional) operator blocks, including the block similarity invariants and the corresponding canonical form. The connection with Kronecker’s theorem about the canonical form of matrix pencils under strict equivalence is discussed. As another application we derive the canonical form under similarity of a non-everywhere defined operator modulo a subspace. For such operators the eigenvalue completion problem is reformulated as a lifting problem.
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© 1995 Birkhäuser Verlag
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Gohberg, I., Kaashoek, M.A., van Schagen, F. (1995). General Blocks. In: Partially Specified Matrices and Operators: Classification, Completion, Applications. Operator Theory Advances and Applications, vol 79. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9100-4_8
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DOI: https://doi.org/10.1007/978-3-0348-9100-4_8
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9906-2
Online ISBN: 978-3-0348-9100-4
eBook Packages: Springer Book Archive