title: Metric invariants of a second-order hypersurface in an n-dimensional Euclidean space
metadata.name: dc.contributor.author
metadata.value: Volkov, Dmitrii Yu.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Galunova, Kseniia V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-07-07T21:19:31Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-07-07T21:19:31Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Volkov D.Yu., Galunova K.V. Metric invariants of a second-order hypersurface in an n-dimensional Euclidean space. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 2, pp. 219–228.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.204
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/37102
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article is devoted to the classical problem of analytic geometry in n-dimensional Euclidean
  space: finding the canonical equation of a quadric. The canonical equation is determined
  by the invariants of the second-order surface equation. Invariants are quantities that
  do not change under an affine change of space coordinates. S. L. Pevsner found a convenient
  system of the following invariants: q is the rank of the extended matrix of the system for determining
  the center of symmetry of the surface; the roots of the characteristic polynomial
  of the matrix of quadratic terms of the surface equation, i. e. the eigenvalues of this matrix;
  Kq is the coefficient of the variable λ to the power of n − q in a polynomial equal to the
  determinant of the n + 1 order matrix obtained by a certain rule from the original surface
  equation. All the coefficients of the canonical equations of quadrics are expressed through
  eigenvalues of the matrix of quadratic terms and the coefficient Kq. Pevsner’s result is
  proved in a new way. Elementary properties of determinants are used in the proof. This
  algorithm for finding the canonical equation of a quadric is a very convenient algorithm for
  computer graphics.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9 (67); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: invariant
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: second-order hypersurfaces
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Metric invariants of a second-order hypersurface in an n-dimensional Euclidean space
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 219-228.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/37102/1/219-228.pdf
resources.format: Adobe PDF
resources.size: 294,53 kB