Fr.: tenseur absolu
A → tensor of → weight → zero.
calculus of tensors
Fr.: calcul tensoriel
The branch of mathematics dealing with the differentiation of tensors.
Fr.: tenseur contravariant
A tensor whose components are distinguished by → superscript indices.
Fr.: tenseur covariant
A tensor whose components are distinguished by → subscript indices.
tânsor-e Einstein (#)
Fr.: tenseur d'Einstein
A mathematical entity describing the → curvature of → space-time in → Einstein's field equations, according to the theory of → general relativity. It is expressed by Gμν = Rμν - (1/2) gμνR, where Rμν is the Ricci tensor, gμν is the → metric tensor, and R the scalar curvature. This tensor is both symmetric and divergence free.
Named after Albert Einstein (1879-1955); → tensor.
Fr.: tenseur énergie-quantité de mouvement
A tensor (Tμν) related to the → Einstein tensor through → Einstein's field equations. The energy-momentum tensor depends upon the distribution of the → energy and → matter in the space.
Fr.: tenseur métrique
The abstract tensor operation which is computed in a particular → reference frame using the → metric components. The metric tensor defines magnitude and direction of vectors about a point.
order of a tensor
Fr.: ordre de tenseur
The maximum number of the indices (→ index) of a tensor.
Fr.: tenseur relatif
A generalized tensor concept that is characterized by a → Jacobian matrix of transformation raised to a power called → weight of a tensor density. In practice, only relative tensors of weight 1 or -1 are used. The product of a relative tensor of weight -1 by another tensor of weight 1 is an → absolute tensor. Same as → tensor density.
Fr.: tenseur de Ricci
A → rank 2, → symmetric tensor Rμν that is a contraction of the → Riemann curvature tensor Rλμνλ. More specifically, Rμν ≡ Σ (λ) Rλμνκ = Rλμνκ. Closely related to the Ricci tensor is the → Einstein tensor, which plays an important role in the theory of → general relativity.
Named after the Italian mathematician Gregorio Ricci-Curbastro (1853-1925); → tensor.
Riemann curvature tensor
tânsor-e xamidegi-ye Riemann
Fr.: tenseur de courbure de Riemann
A 4th → rank tensor that characterizes the deviation of the geometry of space from the Euclidean type. The curvature tensor Rλμνκ is defined through the → Christoffel symbols Γλμν as follows: Rλμνκ = (∂Γλμκ)/(∂xν) - (∂Γλμν)/(∂xκ) + ΓημκΓλην - ΓημνΓληκ.
→ Riemannian geometry; → curvature; → tensor.
Fr.: théorie scalaire-tensorielle
An alternative to the standard → general relativity of gravity that contains not only the → tensor field (or → metric), but also a → scalar field. In this formalism, the → gravitational constant is considered to vary over time. As a consequence, the measured strength of the gravitational interaction is a function of time. Same as → Jordan-Brans-Dicke theory.
Fr.: tenseur antisymétrique
A tensor that is the negative of its → transpose. For example, a second-order covariant tensor Ajk if its components satisfy the equality: Ajk = - Akj. Also called antisymmetric tensor.
→ skew; → symmetric; → tensor.
Fr.: tenseur symétrique
A tensor that is → invariant under any → permutation of its indices (→ index). In other words, a tensor that equals its → transpose. For example, a second-order → covariant tensor Ajk if its components satisfy the equality: Ajk = Akj.
A system of numbers or functions where components obey a certain law of
transformation when the variables undergo a linear transformation.
A tensor may consist of a single number, in which case it is
referred to as a tensor of order zero, or simply a → scalar.
The tensor of order one represents a → vector.
Similarly there will be tensors of order two, three, and so on.
Agent noun of tense (v.) → tension.
Fr.: analyse tensorielle
A method of calculation in higher mathematics based on the properties of tensors.
Fr.: contraction de tenseur
An operation of tensor algebra that is obtained by setting unlike indices equal and summing according to a summation convention.
→ contraction; → tensor.
Fr.: densité de tenseur
A generalization of the tensor concept that like a tensor transforms, except for the appearance of an extra factor, which is the → Jacobian matrix of the transformation of the coordinates, raised to some power, in transformation law. The exponent, which is a positive or negative integer, is called the weight of the tensor density. → weight of a tensor density. Ordinary tensors are tensor densities of weight 0. Tensor density is also called → relative tensor.
Fr.: champ tensoriel
A field of space and time each point of which has multiple directionality, and is describable by a tensor function.
Fr.: perturbation tensorielle
The perturbation in the → primordial Universe plasma caused by → gravitational waves. These waves stretch and squeeze space in orthogonal directions and bring about → quadrupole anisotropy in incoming radiation temperature.
→ tensor; → perturbation.