# Computing hermite forms of polynomial matrices

@inproceedings{Gupta2011ComputingHF,
title={Computing hermite forms of polynomial matrices},
author={Somi Gupta and Arne Storjohann},
booktitle={ISSAC '11},
year={2011}
}
• Published in ISSAC '11 8 June 2011
• Computer Science
This paper presents a new algorithm for computing the Hermite form of a polynomial matrix. Given a nonsingular <i>n</i> x <i>n</i> matrix <i>A</i> filled with degree <i>d</i> polynomials with coefficients from a field, the algorithm computes the Hermite form of <i>A</i> using an expected number of (<i>n</i>3<i>d</i>)<sup>1+o(1)</sup> field operations. This is the first algorithm that is both softly linear in the degree <i>d</i> and softly cubic in the dimension <i>n</i>. The algorithm is…

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