Fast Algorithm for Calculating the Minimal Annihilating Polynomials of Matrices via Pseudo Annihilating Polynomials

Minimal annihilating polynomials are very useful in a wide variety of algorithms in exact linear algebra. A new efficient method is proposed for calculating the minimal annihilating polynomials for all the unit vectors, for a square matrix over a field of characteristic zero. Key ideas of the proposed method are the concept of pseudo annihilating polynomial and the use of binary splitting technique. Efficiency of the resulting algorithms is shown by arithmetic time complexity analysis.