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  2. Del in cylindrical and spherical coordinates - Wikipedia

    en.wikipedia.org/wiki/Del_in_cylindrical_and...

    The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by φ ∈ [ 0 , 2 π ] {\displaystyle \varphi \in [0,2\pi ]} : it is the angle between the x -axis and the projection of the radial vector onto the xy -plane.

  3. Module (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Module_(mathematics)

    A right R-module M R is defined similarly in terms of an operation · : M × R → M. Authors who do not require rings to be unital omit condition 4 in the definition above; they would call the structures defined above "unital left R-modules". In this article, consistent with the glossary of ring theory, all rings and modules are assumed to be ...

  4. Category:Operations on vectors - Wikipedia

    en.wikipedia.org/wiki/Category:Operations_on_vectors

    Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Help; Learn to edit; Community portal; Recent changes; Upload file

  5. Vector calculus - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus

    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.

  6. Vector algebra - Wikipedia

    en.wikipedia.org/wiki/Vector_algebra

    The operations of vector addition and scalar multiplication of a vector space; The algebraic operations in vector calculus (vector analysis) – including the dot and cross products of 3-dimensional Euclidean space; Algebra over a field – a vector space equipped with a bilinear product; Any of the original vector algebras of the nineteenth ...

  7. Array programming - Wikipedia

    en.wikipedia.org/wiki/Array_programming

    These include APL, J, Fortran, MATLAB, Analytica, Octave, R, Cilk Plus, Julia, Perl Data Language (PDL), Raku (programming language). In these languages, an operation that operates on entire arrays can be called a vectorized operation, [1] regardless of whether it is executed on a vector processor, which implements vector instructions. Array ...

  8. Vectorization (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Vectorization_(mathematics)

    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 ...

  9. Curl (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Curl_(mathematics)

    The curl of a vector field F, denoted by curl F, or , or rot F, is an operator that maps C k functions in R 3 to C k−1 functions in R 3, and in particular, it maps continuously differentiable functions R 3 → R 3 to continuous functions R 3 → R 3. It can be defined in several ways, to be mentioned below: