second-order tensor
1Tensor — For other uses, see Tensor (disambiguation). Note that in common usage, the term tensor is also used to refer to a tensor field. Stress, a second order tensor. The tensor s components, in a three dimensional Cartesian coordinate system, form the… …
2Tensor derivative (continuum mechanics) — The derivatives of scalars, vectors, and second order tensors with respect to second order tensors are of considerable use in continuum mechanics. These derivatives are used in the theories of nonlinear elasticity and plasticity, particularly in… …
3Tensor contraction — In multilinear algebra, a tensor contraction is an operation on one or more tensors that arises from the natural pairing of a finite dimensional vector space and its dual. In components, it is expressed as a sum of products of scalar components… …
4Second fundamental form — In differential geometry, the second fundamental form is a quadratic form on the tangent plane of a smooth surface in the three dimensional Euclidean space, usually denoted by II. Together with the first fundamental form, it serves to define… …
5Tensor product — In mathematics, the tensor product, denoted by otimes, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules. In each case the significance of the symbol is the same:… …
6Tensor — Levi Civita Symbol im Dreidimensionalen als Beispiel eines besonders einfachen dreistufigen Tensors Der Tensor ist ein mathematisches Objekt aus der Algebra und Differentialgeometrie. Der Begriff wurde ursprünglich in der Physik eingeführt und… …
7Surface second harmonic generation — is a method for probing interfaces in atomic and molecular systems. In second harmonic generation (SHG), the light frequency is doubled, essentially converting two photons of the original beam of energy E into a single photon of energy 2 E as it… …
8Einstein tensor — The Einstein tensor expresses spacetime curvature in the Einstein field equations for gravitation in the theory of general relativity. It is sometimes called the trace reversed Ricci tensor. Definition In physics and differential geometry, the… …
9Cotton tensor — In differential geometry, the Cotton tensor on a (pseudo) Riemannian manifold of dimension n is a third order tensor concomitant of the metric, like the Weyl tensor. The concept is named after Émile Cotton. Just as the vanishing of the Weyl… …
10Dyadic tensor — In multilinear algebra, a dyadic is a second rank tensor written in a special notation, formed by juxtaposing pairs of vectors, along with a notation for manipulating such expressions analogous to the rules for matrix algebra. Each component of a …
