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... > mathematical analysis > function > elementary function > polynomial > homogeneous polynomial > quadratic form > principal axis theorem
algebra > polynomial > homogeneous polynomial > quadratic form > principal axis theorem
algebra > linear algebra > principal axis theorem
geometry > principal axis theorem

Terme préférentiel

principal axis theorem  

Définition(s)

  • In geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated with an ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular, and gives a constructive procedure for finding them.
    Mathematically, the principal axis theorem is a generalization of the method of completing the square from elementary algebra. In linear algebra and functional analysis, the principal axis theorem is a geometrical counterpart of the spectral theorem. It has applications to the statistics of principal components analysis and the singular value decomposition. In physics, the theorem is fundamental to the studies of angular momentum and birefringence.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Principal_axis_theorem)

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http://data.loterre.fr/ark:/67375/PSR-LP2M5CFX-8

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RDF/XML TURTLE JSON-LD Date de création 28/07/2023, dernière modif. 28/07/2023