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For DTI, it is generally possible to use linear algebra, matrix mathematics and vector mathematics to process the analysis of the tensor data. In some cases, the full set of tensor properties is of interest, but for tractography it is usually necessary to know only the magnitude and orientation of the primary axis or vector. This primary axis ...
Ricci [5] is a system for Mathematica 2.x and later for doing basic tensor analysis, available for free. TTC [6] Tools of Tensor Calculus is a Mathematica package for doing tensor and exterior calculus on differentiable manifolds. EDC and RGTC, [7] "Exterior Differential Calculus" and "Riemannian Geometry & Tensor Calculus," are free ...
A free MATLAB implementation of the TP model transformation can be downloaded at or an old version of the toolbox is available at MATLAB Central . A key underpinning of the transformation is the higher-order singular value decomposition. [7]
The electromagnetic tensor is the combination of the electric and magnetic fields into a covariant antisymmetric tensor whose entries are B-field quantities. [1] = (/ / / / / /) and the result of raising its indices is = = (/ / / / / /), where E is the electric field, B the magnetic field, and c the speed of light.
A (0,1) tensor is a covector. A (0,2) tensor is a bilinear form. An example is the metric tensor . A (1,1) tensor is a linear map. An example is the delta, , which is the identity map, or a Lorentz transformation .
Download QR code; Print/export Download as PDF; Printable version; In other projects ... move to sidebar hide. DTI may refer to: Science and technology . Deep trench ...
The tensor product of two vector spaces is a vector space that is defined up to an isomorphism.There are several equivalent ways to define it. Most consist of defining explicitly a vector space that is called a tensor product, and, generally, the equivalence proof results almost immediately from the basic properties of the vector spaces that are so defined.
A mixed state is described by a density matrix ρ, that is a non-negative trace-class operator of trace 1 on the tensor product . The partial trace of ρ with respect to the system B , denoted by ρ A {\displaystyle \rho ^{A}} , is called the reduced state of ρ on system A .