Numerical techniques for computing the inertia of products of matrices of rational numbers
Proceedings of the 2007 international workshop on Symbolic-numeric computation
The Orbit Problem Is in the GapL Hierarchy
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
The orbit problem is in the GapL hierarchy
Journal of Combinatorial Optimization
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The inertia of an n 脳 n matrix A is defined as the triple(i_ +(A),i_ -(A),i_0 (A)), where i_ +(A),i_ -(A), and i_0 (A) are the number of eigenvalues of A, counting multiplicities, with positive, negative, and zero real part. It is known that the inertia of a large class of matrices can be determined in PL (probabilistic logspace). However, the general problem, whether the inertia of an arbitrary integer matrix is computable in PL, was an open question. In this paper we give a positive answer to this question and show that the problem is complete for PL. As consequences of this result we show necessary and sufficient conditions that certain algebraic functions like the rank or the inertia of an integer matrix can be computed in GapL.