Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 4, Tome 67 (1977), pp. 195-200
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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/
@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
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.
