Cartesian tensor information

algebra, a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components...

of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory...

(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), general relativity (stress–energy tensor, curvature tensor, ...), and...

In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold...

or for expressing a known vector in a different basis. Cartesian tensor Kay, D. C. (1988). Tensor Calculus. Schaum’s Outlines. McGraw Hill. pp. 18–19. ISBN 0-07-033484-6...

two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span V ⊗ W {\displaystyle V\otimes W} in the sense...

tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply stress tensor...

elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor and stiffness...

electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a...

G. The Cartesian product of graphs is not a product in the sense of category theory. Instead, the categorical product is known as the tensor product...

reflecting various orders of complexity. The quadrupole moment tensor Q is a rank-two tensor—3×3 matrix. There are several definitions, but it is normally...

has often been used for Cartesian products of graphs, but is now more commonly used for another construction known as the tensor product of graphs. The...

metric field on M consists of a metric tensor at each point p of M that varies smoothly with p. A metric tensor g is positive-definite if g(v, v) > 0 for...

and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used...

abelian category, is not Cartesian closed. So the category of modules over a ring is not Cartesian closed. However, the functor tensor product − ⊗ M {\displaystyle...

more gradient directions, sufficient to compute the diffusion tensor. The diffusion tensor model is a rather simple model of the diffusion process, assuming...

In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. In components...

unique point. The prototypical example of a coordinate system is the Cartesian coordinate system. In the plane, two perpendicular lines are chosen and...

In graph theory, the tensor product G × H of graphs G and H is a graph such that the vertex set of G × H is the Cartesian product V(G) × V(H); and vertices...

that is, Cartesian tensors of rank 1; and permittivity ε is a Cartesian tensor of rank 2. Strain and stress are, in principle, also rank-2 tensors. But conventionally...

theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in general...

graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which...

example, scalars, vectors, or tensors. Mathematical expressions involving these quantities in vector calculus and tensor analysis (such as the gradient...