Geodesic
A Complete System of Invariants with Respect to Similarity for Pairs of Matrices of Even Order with Characteristic Matrix of Special Smith form
Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 923-941 
B. Z. Shavarovskii. A Complete System of Invariants with Respect to Similarity for Pairs of Matrices of Even Order with Characteristic Matrix of Special Smith form. Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 923-941. http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a13/
@article{MZM_2003_73_6_a13,
     author = {B. Z. Shavarovskii},
     title = {A {Complete} {System} of {Invariants} with {Respect} to {Similarity} for {Pairs} of {Matrices} of {Even} {Order} with {Characteristic} {Matrix} of {Special} {Smith} form},
     journal = {Matemati\v{c}eskie zametki},
     pages = {923--941},
     year = {2003},
     volume = {73},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a13/}
}
TY  - JOUR
AU  - B. Z. Shavarovskii
TI  - A Complete System of Invariants with Respect to Similarity for Pairs of Matrices of Even Order with Characteristic Matrix of Special Smith form
JO  - Matematičeskie zametki
PY  - 2003
SP  - 923
EP  - 941
VL  - 73
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a13/
LA  - ru
ID  - MZM_2003_73_6_a13
ER  - 
%0 Journal Article
%A B. Z. Shavarovskii
%T A Complete System of Invariants with Respect to Similarity for Pairs of Matrices of Even Order with Characteristic Matrix of Special Smith form
%J Matematičeskie zametki
%D 2003
%P 923-941
%V 73
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a13/
%G ru
%F MZM_2003_73_6_a13

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the similarity of a pair of matrices of even order with special Smith form and certain conditions for the decomposability of the characteristic matrix of the pair. In this connection, we obtain a complete system of invariants for this class of pairs of matrices with respect to similarity. The results obtained are stated in the classical terms of ranks, of minimal indices, and of elementary divisors of matrices (both “finite” and “infinite”).

[1] Gelfand I. M., Ponomarev V. A., “Nerazlozhimye predstavleniya gruppy Lorentsa”, UMN, 23:2 (1968), 3–60 | MR | Zbl

[2] Friedland S., “Simultaneous similarity of matrices”, Adv. in Math., 50 (1983), 189–265 | DOI | MR | Zbl

[3] Sergeichuk V. V., Galinskii D. V., “Klassifikatsiya par lineinykh operatorov v chetyrekhmernom vektornom prostranstve”, Beskonechnye gruppy i primykayuschie algebraicheskie struktury, In-t matematiki AN Ukrainy, Kiev, 1993, 413–430 | MR

[4] Ikramov Kh. D., “Ob odnom kriterii kvazidiagonalizuemosti veschestvennykh matrits”, ZhVMiMF, 40:1 (2000), 6–20 | MR | Zbl

[5] Ikramov Kh. D., Chislennoe reshenie matrichnykh uravnenii, Nauka, M., 1984 | Zbl

[6] Kazimirskii P. S., Rozklad matrichnikh mnogochleniv na mnozhniki, Naukova dumka, Kiïv, 1981

[7] Shavarovskii B. Z., “Reduktsiya matrits pri pomoschi ekvivalentnykh i podobnykh preobrazovanii”, Matem. zametki, 64:5 (1998), 769–782 | MR

[8] Kazimirskii P. S., Petrichkovich V. M., “Pro ekvivalentnist polinomialnikh matrits”, Teoretichni ta prikladni pitannya algebri i diferentsialnikh rivnyan, Naukova dumka, Kiïv, 1977, 61–66

[9] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966