Computing the Rank and a Small Nullspace Basis of a Polynomial Matrix

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dc.creatorStorjohann, Arne
dc.creatorVillard, Gilles
dc.date2005-05-11
dc.date.accessioned2026-07-07T03:22:58Z
dc.date.available2026-07-07T03:22:58Z
dc.descriptionWe reduce the problem of computing the rank and a nullspace 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)=softO(n^omega d) operations, with omega the exponent of matrix multiplication over K, then the algorithm uses softO(MM(n,d)) operations in K. The softO notation indicates some missing logarithmic factors. The method is randomized with Las Vegas certification. We achieve our results in part through a combination of matrix Hensel high-order lifting and matrix minimal fraction reconstruction, and through the computation of minimal or small degree vectors in the nullspace seen as a K[x]-module
dc.descriptionResearch Report LIP RR2005-03, January 2005
dc.identifierhttps://arxiv.org/abs/cs/0505030
dc.identifierhttp://arxiv.org/abs/cs/0505030
dc.identifierProceedings of the 2005 International Symposium on Symbolic and Algebraic Computation (2005) 309-316
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/32766
dc.subjectSymbolic Computation
dc.subjectComputational Complexity
dc.subjectI.1; F.2.1
dc.titleComputing the Rank and a Small Nullspace Basis of a Polynomial Matrix
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