Geodesic
On the Interdependence between Invariant Multipliers of a Block-Triangular Matrix and Its Diagonal Blocks
Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 599-612 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The interdependence between the invariant multipliers of a block-triangular matrix and its diagonal blocks is established under some constraints on its canonical diagonal form.
Mots-clés : invariant multipliers of a block-triangular matrix
Keywords: GCD of the minors of a matrix, the group $GL_t(R)$, principal ideal, ring, canonical diagonal form of a matrix. 
@article{MZM_2011_90_4_a8,
     author = {V. P. Shchedrik},
     title = {On the {Interdependence} between {Invariant} {Multipliers} of a {Block-Triangular} {Matrix} and {Its} {Diagonal} {Blocks}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {599--612},
     year = {2011},
     volume = {90},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a8/}
}
TY  - JOUR
AU  - V. P. Shchedrik
TI  - On the Interdependence between Invariant Multipliers of a Block-Triangular Matrix and Its Diagonal Blocks
JO  - Matematičeskie zametki
PY  - 2011
SP  - 599
EP  - 612
VL  - 90
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a8/
LA  - ru
ID  - MZM_2011_90_4_a8
ER  - 
%0 Journal Article
%A V. P. Shchedrik
%T On the Interdependence between Invariant Multipliers of a Block-Triangular Matrix and Its Diagonal Blocks
%J Matematičeskie zametki
%D 2011
%P 599-612
%V 90
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a8/
%G ru
%F MZM_2011_90_4_a8
V. P. Shchedrik. On the Interdependence between Invariant Multipliers of a Block-Triangular Matrix and Its Diagonal Blocks. Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 599-612. http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a8/

[1] W. E. Roth, “The equation $AX-YB=C$ and $AX-XB=C$ in matrices”, Proc. Amer. Math. Soc., 3:3 (1952), 392–396 | MR | Zbl

[2] R. B. Feinberg, “Equivalence of partitioned matrices”, J. Res. Nat. Bur. Standards Sect. B, 80 (1976), 89–97 | MR | Zbl

[3] W. H. Gustafson, “Roth's theorem over commutative rings”, Linear Algebra Appl., 23 (1979), 245–251 | DOI | MR | Zbl

[4] R. E. Hartwig, P. Patricio, “On Roth's pseudo equivalence over rings”, Electron. J. Linear Algebra, 16 (2007), 111–124 | MR | Zbl

[5] I. Kaplansky, “Elementary divisor ring and modules”, Trans. Amer. Math. Soc., 66 (1949), 464–491 | DOI | MR | Zbl

[6] M. Newman, “The Smith normal form of a partitioned matrix”, J. Res. Nat. Bur. Standards Sect. B, 78 (1974), 3–6 | MR | Zbl

[7] L. J. Gerstein, “A local approach to matrix equivalence”, Linear Algebra and Appl., 16:3 (1977), 221–232 | DOI | MR | Zbl