Computing the rank and a small nullspace basis of a polynomial matrix

@article{Storjohann2005ComputingTR,
title={Computing the rank and a small nullspace basis of a polynomial matrix},
author={Arne Storjohann and Gilles Villard},
journal={Proceedings of the 2005 international symposium on Symbolic and algebraic computation},
year={2005}
}
• Published 11 May 2005
• Mathematics, Computer Science
• Proceedings of the 2005 international symposium on Symbolic and algebraic computation
We reduce the problem of computing the rank and a null-space basis of a univariate polynomial matrix to polynomial matrix multiplication. For an input n x n matrix of degree, d over a field K we give a rank and nullspace algorithm using about the same number of operations as for multiplying two matrices of dimension, n and degree, d. If the latter multiplication is done in MM(n,d)= O~(nωd operations, with ω the exponent of matrix multiplication over K, then the algorithm uses O~MM(n,d…
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