Wild problem
In the mathematical areas of linear algebra and representation theory, a problem is wild if it contains the problem of classifying pairs of square matrices up to simultaneous similarity.[1][2][3] Examples of wild problems are classifying indecomposable representations of any quiver that is neither a Dynkin quiver (i.e. the underlying undirected graph of the quiver is a (finite) Dynkin diagram) nor a Euclidean quiver (i.e., the underlying undirected graph of the quiver is an affine Dynkin diagram).[4]
Necessary and sufficient conditions have been proposed to check the simultaneously block triangularization and diagonalization of a finite set of matrices under the assumption that each matrix is diagonalizable over the field of the complex numbers.[5]
See also
References
- ↑ "Representations of partially ordered sets of infinite type", Funkcional'nyi Analiz i ego Priloženija 8 (4): 93–94, 1974
- ↑ Gabriel, P. (1993), "Tame and wild subspace problems", Akademīya Nauk Ukraïni 45 (3): 313–352, doi:10.1007/BF01061008, http://dspace.nbuv.gov.ua/handle/123456789/164555
- ↑ Shavarovskiĭ, B. Z. (2004), "On some "tame" and "wild" aspects of the problem of semiscalar equivalence of polynomial matrices", Matematicheskie Zametki 76 (1): 119–132, doi:10.1023/B:MATN.0000036747.26055.cb
- ↑ Drozd, Yuriy A.; Golovashchuk, Natalia S.; Zembyk, Vasyl V. (2017), "Representations of nodal algebras of type E", Algebra and Discrete Mathematics 23 (1): 16–34
- ↑ Mesbahi, Afshin; Haeri, Mohammad (2015), "Conditions on decomposing linear systems with more than one matrix to block triangular or diagonal form", IEEE Transactions on Automatic Control 60 (1): 233–239, doi:10.1109/TAC.2014.2326292
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