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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 ...
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 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 ...
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
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 the design of algorithms for numerical simulations.
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.
Thus, the TVP of a tensor to a P-dimensional vector consists of P projections from the tensor to a scalar. The projection from a tensor to a scalar is an elementary multilinear projection (EMP). In EMP, a tensor is projected to a point through N unit projection vectors. It is the projection of a tensor on a single line (resulting a scalar ...