Abstract
This paper investigates the Kronecker canonical form of matrix pencils under the genericity assumption that the set of nonzero entries is algebraically independent. We provide a combinatorial characterization of the sums of the row/column indices supported by efficient bipartite matching algorithms. We also give a simple alternative proof for a theorem of Poljak on the generic ranks of matrix powers.
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Iwata, S., Shimizu, R. (2005). Combinatorial Analysis of Generic Matrix Pencils. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_25
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DOI: https://doi.org/10.1007/11496915_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26199-5
Online ISBN: 978-3-540-32102-6
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