Canonical matrices for linear matrix problems

By V. Sergeichuk. 2000

104 citations recorded by the source corpus.

Abstract We consider a large class of matrix problems, which includes the problem of classifying arbitrary systems of linear mappings. For every matrix problem from this class, we construct Belitskii's algorithm for reducing a matrix to a canonical form, which is the generalization of the Jordan normal form, and study the set C mn of indecomposable canonical m×n matrices. Considering C mn as a subset in the affine space of m×n matrices, we prove that either C mn consists of a finite number of points and straight lines for every m×n , or C mn contains a 2-dimensional plane for a certain m×n .

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b1ba04e1abbab34656bb687eec1dd3732b530faf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. G. Belitskii
2. Leiba Rodman
3. Peter Lancaster
4. V. Sergeichuk
5. Roger A. Horn

In Computational Theory and Mathematics

1. G. Belitskii
2. Peter Lancaster
3. Leiba Rodman
4. V. Sergeichuk
5. Fernando De Terán
6. Froilán M. Dopico
7. Roger A. Horn

In Mathematical Physics

1. G. Belitskii
2. Peter Lancaster
3. Leiba Rodman
4. V. Sergeichuk

Citations in the corpus

• Complexity of matrix problems (2003, methodology): “In [26], the entries of matrices in the considered matrix problems satisfied systems of linear equations, for this reason the entries of matrices from T (x) were linear polynomials.”
• Canonical forms for symmetric/skew-symmetric real matrix pairs under strict equivalence and congruence (2005, background): “For a completely different approach to canonical forms of a large class of matrix problems, based on quiver representations, see Sergeichuk [47] and references there.”