Geodesic
Representation of the direct sum of two quadratic fields by rational symmetric matrices
Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 4, Tome 67 (1977), pp. 195-200 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $f$ be a fourth-degree polynomial over the field of rational numbers $\mathbf Q$ with leading coefficient $I$ which decomposes over $\mathbf Q$ into the product of two irreducible second-degree polynomials. It is proved that in order that $f$ be the characteristic polynomial of a symmetric matrix with elements in $\mathbf Q$, it is necessary and sufficient that all the roots of $f$ be real. 
@article{ZNSL_1977_67_a10,
     author = {L. I. Roginskii},
     title = {Representation of the direct sum of two quadratic fields by rational symmetric matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {195--200},
     year = {1977},
     volume = {67},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_67_a10/}
}
TY  - JOUR
AU  - L. I. Roginskii
TI  - Representation of the direct sum of two quadratic fields by rational symmetric matrices
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1977
SP  - 195
EP  - 200
VL  - 67
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1977_67_a10/
LA  - ru
ID  - ZNSL_1977_67_a10
ER  - 
%0 Journal Article
%A L. I. Roginskii
%T Representation of the direct sum of two quadratic fields by rational symmetric matrices
%J Zapiski Nauchnykh Seminarov POMI
%D 1977
%P 195-200
%V 67
%U http://geodesic.mathdoc.fr/item/ZNSL_1977_67_a10/
%G ru
%F ZNSL_1977_67_a10
L. I. Roginskii. Representation of the direct sum of two quadratic fields by rational symmetric matrices. Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 4, Tome 67 (1977), pp. 195-200. http://geodesic.mathdoc.fr/item/ZNSL_1977_67_a10/