Fast parallel computation of hermite and smith forms of polynomial matrices
SIAM Journal on Algebraic and Discrete Methods
Why is Boolean complexity theory difficult?
Poceedings of the London Mathematical Society symposium on Boolean function complexity
An O(n3) algorithm for the Frobenius normal form
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Modern computer algebra
Verifying the determinant in parallel
Computational Complexity
The complexity of matrix rank and feasible systems of linear equations
Computational Complexity
The Complexity of Verifying the Characteristic Polynomial and Testing Similarity
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
On the Minimal Polynomial of a Matrix
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
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We investigate the computational complexity of the minimal polynomial of an integer matrix. We show that the computation of the minimal polynomial is in AC0(GapL), the AC0-closure of the logspace counting class GapL, which is contained in NC2. Our main result is that the problem is hard for GapL (under AC0 many-one reductions). The result extends to the verification of all invariant factors of an integer matrix. Furthermore, we consider the complexity to check whether an integer matrix is diagonalizable. We show that this problem lies in AC0(GapL) and is hard for AC0(C=L) (under AC0 many-one reductions).