The Complexity of Verifying the Characteristic Polynomial and Testing Similarity

Authors:
Thanh Minh Hoang;Thomas Thierauf
Affiliations:
-;-
Venue:
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Year:
2000

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Abstract

We investigate the computational complexity of some important problems in linear algebra. 1. The problem of verifying the characteristic polynomial of a matrix is known to be in the complexity class C=L (Exact Counting in Logspace). We show that it is complete for C=L under logspace many-one reductions. 2. The problem of deciding whether two matrices are similar is known to be in the complexity class AC0 (C=L). We show that it is complete for this class under logspace many-one reductions. We also consider the problems of deciding equivalence and congruence of matrices.