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In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .
The dotted vector, in this case B, is differentiated, while the (undotted) A is held constant. The utility of the Feynman subscript notation lies in its use in the derivation of vector and tensor derivative identities, as in the following example which uses the algebraic identity C⋅(A×B) = (C×A)⋅B:
In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.
Vector notation and linear algebra currently used to write these formulas were not yet available at the time of their discovery. The tangent, normal, and binormal unit vectors, often called T , N , and B , or collectively the Frenet–Serret frame ( TNB frame or TNB basis ), together form an orthonormal basis that spans R 3 , {\displaystyle ...
The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .
Vector Analysis, a textbook on vector calculus by Wilson, first published in 1901, which did much to standardize the notation and vocabulary of three-dimensional linear algebra and vector calculus Vector bundle , a topological construction that makes precise the idea of a family of vector spaces parameterized by another space
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.
Added description of what each notation represents~~~~ 23:45, 23 April 2015: 512 × 195 (508 bytes) Krishnavedala: fill circle and then put cross symbol: 23:42, 23 April 2015: 512 × 195 (507 bytes) Krishnavedala: much reduced: 18:02, 5 February 2014: 110 × 42 (660 bytes) Krishnavedala: Hand drawn, smaller size, smoother rendering, added info ...