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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.
For example, Slicer's DTI package allows the conversion and analysis of DTI images. The results of such analysis can be integrated with the results from analysis of morphologic MRI, MR angiograms and fMRI. Other uses of Slicer include paleontology [14] and neurosurgery planning. [15] There is an active community at Slicer's Discourse server. [16]
For example, in the Pascal programming language, the declaration type MyTable = array [1.. 4, 1.. 2] of integer, defines a new array data type called MyTable. The declaration var A: MyTable then defines a variable A of that type, which is an aggregate of eight elements, each being an integer variable identified by two indices.
Eigen is a high-level C++ library of template headers for linear algebra, matrix and vector operations, geometrical transformations, numerical solvers and related algorithms. Eigen is open-source software licensed under the Mozilla Public License 2.0 since version 3.1.1. Earlier versions were licensed under the GNU Lesser General Public License ...
In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable or defined over a multi-dimensional domain. [1] A common special case is bivariate interpolation or two-dimensional interpolation, based on two variables or two dimensions.
A three-dimensional vector can be described with three components: its projection on the x, y, and z axes. Vectors of this sort can be considered tensors of rank 1, or 1st-order tensors. A tensor is often a physical or biophysical property that determines the relationship between two vectors. When a force is applied to an object, movement can ...
If V is a finite-dimensional vector space, a dyadic tensor on V is an elementary tensor in the tensor product of V with its dual space. The tensor product of V and its dual space is isomorphic to the space of linear maps from V to V: a dyadic tensor vf is simply the linear map sending any w in V to f(w)v.
For r > 2 there are hyperdeterminants with different formats satisfying the format inequality. For example, Cayley's 2 × 2 × 2 hyperdeterminant has format (1, 1, 1) and a 2 × 2 × 3 hyperdeterminant of format (1, 1, 2) also exists. However a 2 × 2 × 4 hyperdeterminant would have format (1, 1, 3) but 3 > 1 + 1 so it does not exist.