Geodesic
Invarianty i Kanonicheskie Uravneniya Giperpoverhnosti Vtorogo Poryadka v N-mernom Evklidovom Prostranstve
Publications de l'Institut Mathématique, _N_S_55 (1994) no. 69, p. 75

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The complete solution of the problem of finding invariants and canonical equations of quadrics (hypersurfaces of second order) in $n$-dimensional Euclidean space is given. The square matrix $A$ of the coefficients of second order terms of a quadric equation, and the rectangular matrix $D$ obtained from $A$ by adding of the column of the coefficients of first order terms, are considered. The ranks $r$ and $q$ of these matrices are invariants of a quadric; if $r=q$, then the quadric is central, if $r+1=q$ it is parabolic. An invariant $\Gamma_q$, which is a coefficient of a polynomial, is introduced. All the coefficients of the canonical equation of a quadric are expressed through eigenvalues of the matrix A and the invariant $\Gamma_q$. The problem is solved without "semi-invariants".
Classification : 53A07 53A55 
@article{PIM_1994_N_S_55_69_a9,
     author = {S.L. Pevzner},
     title = {Invarianty i {Kanonicheskie} {Uravneniya} {Giperpoverhnosti} {Vtorogo} {Poryadka} v {N-mernom} {Evklidovom} {Prostranstve}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {75 },
     publisher = {mathdoc},
     volume = {_N_S_55},
     number = {69},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a9/}
}
TY  - JOUR
AU  - S.L. Pevzner
TI  - Invarianty i Kanonicheskie Uravneniya Giperpoverhnosti Vtorogo Poryadka v N-mernom Evklidovom Prostranstve
JO  - Publications de l'Institut Mathématique
PY  - 1994
SP  - 75 
VL  - _N_S_55
IS  - 69
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a9/
LA  - en
ID  - PIM_1994_N_S_55_69_a9
ER  - 
%0 Journal Article
%A S.L. Pevzner
%T Invarianty i Kanonicheskie Uravneniya Giperpoverhnosti Vtorogo Poryadka v N-mernom Evklidovom Prostranstve
%J Publications de l'Institut Mathématique
%D 1994
%P 75 
%V _N_S_55
%N 69
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a9/
%G en
%F PIM_1994_N_S_55_69_a9
S.L. Pevzner. Invarianty i Kanonicheskie Uravneniya Giperpoverhnosti Vtorogo Poryadka v N-mernom Evklidovom Prostranstve. Publications de l'Institut Mathématique, _N_S_55 (1994) no. 69, p. 75 . http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a9/