A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional...
18 KB (3,000 words) - 20:11, 9 May 2024
An infinite-dimensional vector function is a function whose values lie in an infinite-dimensional topological vector space, such as a Hilbert space or...
9 KB (1,427 words) - 07:19, 23 April 2023
(which represents the rotation of a flow). A vector field is a special case of a vector-valued function, whose domain's dimension has no relation to the...
28 KB (4,070 words) - 03:02, 14 July 2024
known as vector resolute or vector component, a linear mapping producing a vector parallel to a second vector Vector-valued function, a function that has...
10 KB (2,013 words) - 17:06, 9 August 2024
of the mean value theorem to vector-valued functions is obtained as follows: Let f be a continuously differentiable real-valued function defined on an...
35 KB (6,867 words) - 13:59, 2 August 2024
In vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order...
25 KB (3,593 words) - 19:18, 22 August 2024
example, the function that associates to each point of a fluid its velocity vector is a vector-valued function. Some vector-valued functions are defined...
75 KB (11,265 words) - 19:54, 30 July 2024
vector) Tensor Unit vector Vector bundle Vector calculus Vector notation Vector-valued function Ivanov 2001 Heinbockel 2001 Itô 1993, p. 1678; Pedoe 1988...
60 KB (9,031 words) - 07:53, 25 June 2024
the inverse function. In multivariable calculus, this theorem can be generalized to any continuously differentiable, vector-valued function whose Jacobian...
39 KB (7,303 words) - 00:11, 8 August 2024
member of its domain. Real-valued functions of a real variable (commonly called real functions) and real-valued functions of several real variables are...
8 KB (993 words) - 15:40, 22 June 2023