Abstract
We investigate the computational complexity of the minimal polynomial of an integer matrix.
We show that the computation of the minimal polynomial is in AC 0(GapL), the AC 0-closure of the logspace counting class GapL, which is contained in NC 2. Our main result is that the problem is hard for GapL (under AC 0 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 AC 0(GapL) and is hard for AC 0(C = L) (under AC 0 many-one reductions).
This work was supported by the Deutsche Forschungsgemeinschaft
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Hoang, T.M., Thierauf, T. (2001). The Complexity of the Minimal Polynomial. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_36
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DOI: https://doi.org/10.1007/3-540-44683-4_36
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