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

• Semi-invariant of a quiver