trace of tensor
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Tensor 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… … Wikipedia
Trace (linear algebra) — In linear algebra, the trace of an n by n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii represents the entry on the ith row and ith column … Wikipedia
Tensor — 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… … Wikipedia
Trace diagram — In mathematics, trace diagrams are a graphical means of performing computations in linear and multilinear algebra. They can be represented as graphs with edges labeled by matrices. Without the matrix labels, they are equivalent to Penrose s… … Wikipedia
Cotton 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… … Wikipedia
Einstein 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… … Wikipedia
Torsion tensor — In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The torsion of a curve, as it appears in the Frenet Serret formulas, for instance, quantifies the twist of a curve… … Wikipedia
Weyl tensor — In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal… … Wikipedia
Riemann tensor (general relativity) — The Riemann tensor (general relativity) is a mathematical object that describes gravitation and its effects in Einstein s theory of general relativity. Curvature and geodesic deviationThe Riemann tensor can be used to express the idea of… … Wikipedia
Partial trace — In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is an operator valued function. The partial trace has applications in… … Wikipedia
Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… … Wikipedia
