On computing the determinant in small parallel time using a small number of processors
Information Processing Letters
Matrix analysis
Topics in matrix analysis
The design and analysis of algorithms
The design and analysis of algorithms
Why is Boolean complexity theory difficult?
Poceedings of the London Mathematical Society symposium on Boolean function complexity
Gap-definable counting classes
Journal of Computer and System Sciences
Specified precision polynomial root isolation is in NC
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
An efficient algorithm for the complex roots problem
Journal of Complexity
SIAM Journal on Computing
Verifying the determinant in parallel
Computational Complexity
The complexity of matrix rank and feasible systems of linear equations
Computational Complexity
Exact computations of the inertia symmetric integer matrices
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Complexity of the Minimal Polynomial
MFCS '01 Proceedings of the 26th International Symposium on 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
Numerical techniques for computing the inertia of products of matrices of rational numbers
Proceedings of the 2007 international workshop on Symbolic-numeric computation
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The inertia of a square matrix A is defined as the triple (i+(A), i-(A), i0(A)), where i+(A), i-(A), and i0(A) are the number of eigenvalues of A, counting multiplicities, with positive, negative, and zero real part, respectively. A hard problem in Linear Algebra is to compute the inertia. No method is known to get the inertia of a matrix exactly in general. In this paper we show that the inertia is hard for PL (probabilistic logspace) and in some cases the inertia can be computed in PL. We extend our result to some problems related to the inertia. Namely, we show that matrix stability is complete for PL and the inertia of symmetric matrices can be computed in PL.