Geodesic
The congruence centralizer of a block diagonal matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIX, Tome 453 (2016), pp. 96-103 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let a complex matrix $A$ be the direct sum of its square submatrices $B$ and $C$ that have no common eigenvalues. Then every matrix $X$ belonging to the centralizer of $A$ has the same block diagonal form as the matrix $A$ itself. In this paper, we discuss how the conditions on the submatrices $B$ and $C$ should be modified to make valid an analogous statement about the congruence centralizer of $A$, which is the set of matrices $X$ such that $X^*AX=A$. We also consider the question whether the matrices in the congruence centralizer are block diagonal if $A$ is a block antidiagonal matrix. 
@article{ZNSL_2016_453_a6,
     author = {Kh. D. Ikramov},
     title = {The congruence centralizer of a~block diagonal matrix},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {96--103},
     year = {2016},
     volume = {453},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a6/}
}
TY  - JOUR
AU  - Kh. D. Ikramov
TI  - The congruence centralizer of a block diagonal matrix
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 96
EP  - 103
VL  - 453
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a6/
LA  - ru
ID  - ZNSL_2016_453_a6
ER  - 
%0 Journal Article
%A Kh. D. Ikramov
%T The congruence centralizer of a block diagonal matrix
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 96-103
%V 453
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a6/
%G ru
%F ZNSL_2016_453_a6
Kh. D. Ikramov. The congruence centralizer of a block diagonal matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIX, Tome 453 (2016), pp. 96-103. http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a6/