Reduction of Matrix Polynomials to Simpler Forms

@article{Nakatsukasa2018ReductionOM,
  title={Reduction of Matrix Polynomials to Simpler Forms},
  author={Yuji Nakatsukasa and Leo Taslaman and Françoise Tisseur and Ion Zaballa},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2018},
  volume={39},
  pages={148-177}
}
A square matrix can be reduced to simpler form via similarity transformations. Here “simpler form” may refer to diagonal (when possible), triangular (Schur), or Hessenberg form. Similar reductions exist for matrix pencils if we consider general equivalence transformations instead of similarity transformations. For both matrices and matrix pencils, well-established algorithms are available for each reduction, which are useful in various applications. For matrix polynomials, unimodular… 

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