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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 ...
The tensor can be flattened in three ways to obtain matrices comprising its mode-0, mode-1, and mode-2 vectors. [ 1 ] In multilinear algebra , mode-m flattening [ 1 ] [ 2 ] [ 3 ] , also known as matrixizing , matricizing , or unfolding , [ 4 ] is an operation that reshapes a multi-way array A {\displaystyle {\mathcal {A}}} into a matrix denoted ...
Tensor [4] is a tensor package written for the Mathematica system. It provides many functions relevant for General Relativity calculations in general Riemann–Cartan geometries. Ricci [5] is a system for Mathematica 2.x and later for doing basic tensor analysis, available for free.
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.
Diffusion tensor imaging, a structural medical imaging technique; Direct thrombin inhibitor; Diesel turbo injection, a brand name for common rail; Direct tension indicator; Deep tissue injury, see suspected deep tissue injury in List of medical abbreviations: S; Dye transfer inhibitor
In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar, while the cross product [a] returns a pseudovector.
For a 3rd-order tensor , where is either or , Tucker Decomposition can be denoted as follows, = () where is the core tensor, a 3rd-order tensor that contains the 1-mode, 2-mode and 3-mode singular values of , which are defined as the Frobenius norm of the 1-mode, 2-mode and 3-mode slices of tensor respectively.
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