792 research outputs found
Complexity of matrix problems
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.Comment: 24 page
Computation of the canonical form for the matrices of chains and cycles of linear mappings
Paul Van Dooren [Linear Algebra Appl. 27 (1979) 103-140] constructed an
algorithm for the computation of all irregular summands in Kronecker's
canonical form of a matrix pencil. The algorithm is numerically stable since it
uses only unitary transformations. We extend Paul Van Dooren's algorithm to the
matrices of a cycle of linear mappings.Comment: 34 page
Quantum-chemical modeling of the electronic structure of aromatic hydrocarbons of catalytic cracking of vacuum distillate
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