TY - JOUR
T1 - Complexity of matrix problems
AU - Belitskii, Genrich R.
AU - Sergeichuk, Vladimir V.
N1 - Funding Information:
*Corresponding author. E-mail addresses: [email protected] (G.R. Belitskii), [email protected] (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 -