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Segre classification

Index Segre classification

The Segre classification is an algebraic classification of rank two symmetric tensors. [1]

8 relations: Cambridge University Press, Corrado Segre, Exact solutions in general relativity, Jordan normal form, Petrov classification, Ricci curvature, Stress–energy tensor, Symmetric tensor.

Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Corrado Segre

Corrado Segre (20 August 1863 – 18 May 1924) was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry.

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Exact solutions in general relativity

In general relativity, an exact solution is a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field.

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Jordan normal form

In linear algebra, a Jordan normal form (often called Jordan canonical form) of a linear operator on a finite-dimensional vector space is an upper triangular matrix of a particular form called a Jordan matrix, representing the operator with respect to some basis.

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Petrov classification

In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold.

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Ricci curvature

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a small wedge of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.

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Stress–energy tensor

The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.

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Symmetric tensor

In mathematics, a symmetric tensor is a tensor that is invariant under a permutation of its vector arguments: for every permutation σ of the symbols Alternatively, a symmetric tensor of order r represented in coordinates as a quantity with r indices satisfies The space of symmetric tensors of order r on a finite-dimensional vector space is naturally isomorphic to the dual of the space of homogeneous polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is that of the antisymmetric tensor or alternating form.

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References

[1] https://en.wikipedia.org/wiki/Segre_classification

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