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Download as PDF; Printable version; In other projects ... Pages in category "Operations on vectors" The following 16 pages are in this category, out of 16 total ...
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication.
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 ...
where r is the radial distance, φ is the azimuthal angle and θ is the polar angle, and e r, e θ and e φ are again local unit vectors pointing in the coordinate directions (that is, the normalized covariant basis). For the gradient in other orthogonal coordinate systems, see Orthogonal coordinates (Differential operators in three dimensions).
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract. A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations.
For Minkowski addition, the zero set, {}, containing only the zero vector, 0, is an identity element: for every subset S of a vector space, S + { 0 } = S . {\displaystyle S+\{0\}=S.} The empty set is important in Minkowski addition, because the empty set annihilates every other subset: for every subset S of a vector space, its sum with the ...
In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the ...