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. 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
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the classification of semisimple Lie algebras ...
).
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.
See also
*
Semi-invariant of a quiver
In mathematics, given a Quiver (mathematics), quiver Q with set of vertices Q0 and set of arrows Q1, a representation (mathematics), representation of Q assigns a vector space ''V'i'' to each vertex and a linear map ''V''(''α''): ''V''(''s''('' ...
References
Linear algebra
Representation theory
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