Complexity of matrix problems

Details Complexity of matrix problems Complexity of matrix problems

2007-09-16

arxiv.org/abs/0709.2488v1

Linear Algebra Appl. 361 (2003) 203-222

Mathematics

Representation Theory

24 pages

Scientific paper

10.1016/S0024-3795(02)00391-9

In representation theory, the problem of classifying pairs of matrices up to simultaneous similarity is used as a measure of complexity; classification problems containing it are called wild problems. We show in an explicit form that this problem contains all classification matrix problems given by quivers or posets. Then we prove that it does not contain (but is contained in) the problem of classifying three-valent tensors. Hence, all wild classification problems given by quivers or posets have the same complexity; moreover, a solution of any one of these problems implies a solution of each of the others. The problem of classifying three-valent tensors is more complicated.

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