Search results
Results From The WOW.Com Content Network
In mathematics, vector algebra may mean: 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
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.
Given a subset S of R n, a vector field is represented by a vector-valued function V: S → R n in standard Cartesian coordinates (x 1, …, x n).If each component of V is continuous, then V is a continuous vector field.
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.
For instance, the points A = (1, 0, 0) and B = (0, 1, 0) in space determine the bound vector pointing from the point x = 1 on the x-axis to the point y = 1 on the y-axis. In Cartesian coordinates, a free vector may be thought of in terms of a corresponding bound vector, in this sense, whose initial point has the coordinates of the origin O = (0 ...
The set of complex numbers C, numbers that can be written in the form x + iy for real numbers x and y where i is the imaginary unit, form a vector space over the reals with the usual addition and multiplication: (x + iy) + (a + ib) = (x + a) + i(y + b) and c ⋅ (x + iy) = (c ⋅ x) + i(c ⋅ y) for real numbers x, y, a, b and c. The various ...
In the linear case the function can be expressed in terms of matrices: =, where y is an n × 1 output vector, x is a k × 1 vector of inputs, and A is an n × k matrix of parameters. Closely related is the affine case (linear up to a translation ) where the function takes the form y = A x + b , {\displaystyle \mathbf {y} =A\mathbf {x} +\mathbf ...
Christiaan Huygens, a talented mathematician and physicist and older contemporary of Newton, was the first to successfully idealize a physical problem by a set of mathematical parameters in Horologium Oscillatorum (1673), and the first to fully mathematize a mechanistic explanation of an unobservable physical phenomenon in Traité de la ...