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Function rank is an important concept to array programming languages in general, by analogy to tensor rank in mathematics: functions that operate on data may be classified by the number of dimensions they act on. Ordinary multiplication, for example, is a scalar ranked function because it operates on zero-dimensional data (individual numbers).
For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal. For such matrices, the half-vectorization is sometimes more useful than the ...
In computer graphics, swizzles are a class of operations that transform vectors by rearranging components. [1] Swizzles can also project from a vector of one dimensionality to a vector of another dimensionality, such as taking a three-dimensional vector and creating a two-dimensional or five-dimensional vector using components from the original vector. [2]
Vector combine Rotate & move Polylines Spline curves Lines to curves cmd. & vice versa Vector shapes Easy Trace Yes Yes Yes Yes Yes Yes Yes Graphic Tracer Professional N/A Yes Yes Yes Yes Yes Yes Adobe Illustrator Yes Yes Yes Yes Yes No Yes Potrace N/A N/A N/A N/A N/A N/A N/A ImageTracer N/A N/A N/A N/A N/A N/A N/A Scan2CAD Yes Yes Yes Yes Yes Yes
The components of a vector are often represented arranged in a column. By contrast, a covector has components that transform like the reference axes. It lives in the dual vector space, and represents a linear map from vectors to scalars. The dot product operator involving vectors is a good example of a covector.
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SPLATT [1] is an open source software package for high-performance sparse tensor factorization. SPLATT ships a stand-alone executable, C/C++ library, and Octave / MATLAB API . Cadabra [ 2 ] is a computer algebra system (CAS) designed specifically for the solution of problems encountered in field theory.
A graph of the vector-valued function r(z) = 2 cos z, 4 sin z, z indicating a range of solutions and the vector when evaluated near z = 19.5. A common example of a vector-valued function is one that depends on a single real parameter t, often representing time, producing a vector v(t) as the result.