Geodesic
On the codimension of the variety of symmetric matrices with multiple eigenvalues
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 34-46 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

According to a result of Wigner and von Neumann, the dimension of the set $\mathcal M$ of $n\times n$ real symmetric matrices with multiple eigenvalues is equal to $N-2$, where $N=n(n+1)/2$. This value is determined by counting the number of free parameters in the spectral decomposition of a matrix. We show that the same dimension is obtained if $\mathcal M$ is interpreted as an algebraic variety. 
@article{ZNSL_2005_323_a3,
     author = {M. Dana and Kh. D. Ikramov},
     title = {On the codimension of the variety of symmetric matrices with multiple eigenvalues},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {34--46},
     year = {2005},
     volume = {323},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a3/}
}
TY  - JOUR
AU  - M. Dana
AU  - Kh. D. Ikramov
TI  - On the codimension of the variety of symmetric matrices with multiple eigenvalues
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 34
EP  - 46
VL  - 323
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a3/
LA  - ru
ID  - ZNSL_2005_323_a3
ER  - 
%0 Journal Article
%A M. Dana
%A Kh. D. Ikramov
%T On the codimension of the variety of symmetric matrices with multiple eigenvalues
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 34-46
%V 323
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a3/
%G ru
%F ZNSL_2005_323_a3
M. Dana; Kh. D. Ikramov. On the codimension of the variety of symmetric matrices with multiple eigenvalues. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 34-46. http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a3/

[1] P. Lax, Linear Algebra, Wiley, New York, 1997 | MR

[2] Kh. D. Ikramov, “O razmernosti mnogoobraziya simmetrichnykh matrits s kratnymi sobstvennymi znacheniyami”, Zh. vychisl. matem. matem. fiz., 44 (2004), 963–967 | MR | Zbl

[3] N. V. Ilyushechkin, “Diskriminant kharakteristicheskogo mnogochlena normalnoi matritsy”, Mat. zametki, 51 (1992), 16–23 | MR | Zbl

[4] B. N. Parlett, “The (matrix) discriminant as a determinant”, Linear Algebra Appl., 355 (2002), 85–101 | DOI | MR | Zbl