Computing Minimal Polynomials of Matrices
2008 ◽
Vol 11
◽
pp. 252-279
◽
Keyword(s):
AbstractWe present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of ann × nmatrix over a finite field that requiresO(n3) field operations andO(n) random vectors, and is well suited for successful practical implementation. The algorithm, and its complexity analysis, use standard algorithms for polynomial and matrix operations. We compare features of the algorithm with several other algorithms in the literature. In addition we present a deterministic verification procedure which is similarly efficient in most cases but has a worst-case complexity ofO(n4). Finally, we report the results of practical experiments with an implementation of our algorithms in comparison with the current algorithms in the GAP library.
Keyword(s):
1992 ◽
Vol 42
(3)
◽
pp. 145-149
◽
Keyword(s):
1998 ◽
Vol 19
(3-4)
◽
pp. 329-343
◽
2012 ◽
Vol 1
(1-2)
◽
pp. 143-153
◽