Combinatorial Analysis of Singular Matrix Pencils
Satoru Iwata, Ryo Shimizu · SIAM Journal on Matrix Analysis and Applications · 2007
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.