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Armadillo [2] [3] NICTA: C++ 2009 12.6.6 / 10.2023 Free Apache License 2.0: C++ template library for linear algebra; includes various decompositions and factorisations; syntax is similar to MATLAB. ATLAS: R. Clint Whaley et al. C 2001 3.10.3 / 07.2016 Free BSD Automatically tuned implementation of BLAS. Also includes LU and Cholesky decompositions.
Download QR code; Print/export Download as PDF; Printable version; ... Help. Pages in category "Operations on vectors" The following 16 pages are in this category ...
The elementary functions are constructed by composing arithmetic operations, the exponential function (), the natural logarithm (), trigonometric functions (,), and their inverses. The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's ...
These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space. Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. [7]
A scalar is an element of a field which is used to define a vector space.In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector.
Binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, and exponentiation. [4] Operations can involve mathematical objects other than numbers. The logical values true and false can be combined using logic operations, such as and, or, and not. Vectors can be added and subtracted. [5]
Interval arithmetic – Method for bounding the errors of numerical computations; Mixed volume (a.k.a. Quermassintegral or intrinsic volume) Parallel curve – Generalization of the concept of parallel lines; Shapley–Folkman lemma – Sums of sets of vectors are nearly convex; Sumset – Set of pairwise sums of elements of two sets
Let p = (p 1, p 2) be an element of W, that is, a point in the plane such that p 1 = p 2, and let c be a scalar in R. Then cp = (cp 1, cp 2); since p 1 = p 2, then cp 1 = cp 2, so cp is an element of W. In general, any subset of the real coordinate space R n that is defined by a homogeneous system of linear equations will yield a subspace.