Matrix Polynomials with Completely Prescribed Eigenstructure

@article{Tern2015MatrixPW,
  title={Matrix Polynomials with Completely Prescribed Eigenstructure},
  author={F. Ter{\'a}n and F. Dopico and P. Dooren},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2015},
  volume={36},
  pages={302-328}
}
We present necessary and sufficient conditions for the existence of a matrix polynomial when its degree, its finite and infinite elementary divisors, and its left and right minimal indices are prescribed. These conditions hold for arbitrary infinite fields and are determined mainly by the “index sum theorem,” which is a fundamental relationship between the rank, the degree, the sum of all partial multiplicities, and the sum of all minimal indices of any matrix polynomial. The proof developed… Expand
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