TY - JOUR

T1 - Complexity of matrix problems

AU - Belitskii, Genrich R.

AU - Sergeichuk, Vladimir V.

N1 - Funding Information:
*Corresponding author. E-mail addresses: genrich@indigo.cs.bgu.ac.il (G.R. Belitskii), sergeich@ukrpack.net (V.V. Sergei-chuk). 1 Partially supported by Israel Science Foundation, Grant 216/98. 2Partially supported by NSF grant DMS-0070503. The research was started while this author was visiting the Ben-Gurion University of the Negev supported by Israel Science Foundation.

PY - 2003/3/1

Y1 - 2003/3/1

N2 - In representation theory, the classification problem is called wild if it contains the problem of classifying pairs of matrices up to simultaneous similarity. We show in an explicit form that the last problem contains all classification matrix problems given by quivers or posets. Then we prove that this problem does not contain (but is contained in) the problem of classifying three-valent tensors. Hence, every wild classification problem given by a quiver or poset has the same complexity; moreover, a solution of one of them implies a solution of each of the remaining problems. The problem of classifying three-valent tensors is more complicated.

AB - In representation theory, the classification problem is called wild if it contains the problem of classifying pairs of matrices up to simultaneous similarity. We show in an explicit form that the last problem contains all classification matrix problems given by quivers or posets. Then we prove that this problem does not contain (but is contained in) the problem of classifying three-valent tensors. Hence, every wild classification problem given by a quiver or poset has the same complexity; moreover, a solution of one of them implies a solution of each of the remaining problems. The problem of classifying three-valent tensors is more complicated.

KW - Canonical matrices

KW - Classification

KW - Representations of quivers and posets

KW - Tame and wild matrix problems

KW - Tensors

UR - http://www.scopus.com/inward/record.url?scp=84867963920&partnerID=8YFLogxK

U2 - 10.1016/S0024-3795(02)00391-9

DO - 10.1016/S0024-3795(02)00391-9

M3 - Article

AN - SCOPUS:84867963920

SN - 0024-3795

VL - 361

SP - 203

EP - 222

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -