Matrix Rank Certification

David Saunders (1) , Arne Storjohann (1) , Gilles Villard (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

Randomized algorithms are given for computing the rank of a matrix over a field of characteristic zero. The matrix is treated as a black box. Only the capability to compute matrix x column-vector and row-vector x matrix products is used. The methods are exact, sometimes called seminumeric. They are appropriate for example for matrices with integer or rational entries. The rank algorithms are probabilistic of the Las Vegas type; the correctness of the result is guaranteed.

Mots clés: Black Box Matrix; Linear Algebra; Matrix Rank; Randomized Algorithms; Seminumeric Computation

Domaines: Informatique [cs]

David Saunders, Arne Storjohann, Gilles Villard. Matrix Rank Certification. [Research Report] LIP RR-2001-30, Laboratoire de l'informatique du parallélisme. 2001, 2+6p. ⟨hal-02102007⟩