On computing the determinant in small parallel time using a small number of processors
Information Processing Letters
Matrix analysis
Topics in matrix analysis
The method of forced enumeration for nondeterministic automata
Acta Informatica
Nondeterministic space is closed under complementation
SIAM Journal on Computing
Why is Boolean complexity theory difficult?
Poceedings of the London Mathematical Society symposium on Boolean function complexity
The complexity of matrix rank and feasible systems of linear equations
Computational Complexity
Making Nondeterminism Unambiguous
SIAM Journal on Computing
The Complexity of the Minimal Polynomial
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
The complexity of the characteristic and the minimal polynomial
Theoretical Computer Science - Mathematical foundations of computer science
The Complexity of Verifying the Characteristic Polynomial and Testing Similarity
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
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We investigate the complexity of the degree and the constant term of the minimal polynomial of a matrix. We show that the degree of the minimal polynomial behaves as the matrix rank.We compare the constant term of the minimal polynomial with the constant term of the characteristic polynomial. The latter is known to be computable in the logspace counting class GapL. We show that this holds also for the minimal polynomial if and only if the logspace exact counting class C=L is closed under complement. The latter condition is one of the main open problems in this area.As an application of our techniques we show that the problem to decide whether a matrix is diagonalizable is complete for AC0(C=L), the AC0- closure of C=L.