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In the theory of vector measures, Lyapunov's theorem states that the range of a finite-dimensional vector measure is closed and convex. [ 1 ] [ 2 ] [ 3 ] In fact, the range of a non-atomic vector measure is a zonoid (the closed and convex set that is the limit of a convergent sequence of zonotopes ). [ 2 ]
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.
Originally, many thước of varying lengths were in use in Vietnam, each used for different purposes. According to Hoàng Phê (1988), [1] the traditional system of units had at least two thước of different lengths before 1890, [2] the thước ta (lit. "our ruler") or thước mộc ("wooden ruler"), equal to 0.425 metres (1 ft 4.7 in), and the thước đo vải ("ruler for measuring ...
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 vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater than 1); the ...
Every vector a in three dimensions is a linear combination of the standard basis vectors i, j and k. In mathematics , the standard basis (also called natural basis or canonical basis ) of a coordinate vector space (such as R n {\displaystyle \mathbb {R} ^{n}} or C n {\displaystyle \mathbb {C} ^{n}} ) is the set of vectors, each of whose ...
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,
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.