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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.
A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction.
In Poynting's original paper and in most textbooks, the Poynting vector is defined as the cross product [4] [5] [6] =, where bold letters represent vectors and . E is the electric field vector;
Vector (molecular biology), a DNA molecule used as a vehicle to artificially carry foreign genetic material into another cell Cloning vector, a small piece of DNA into which a foreign DNA fragment can be inserted for cloning purposes
In this article, vectors are represented in boldface to distinguish them from scalars. [nb 1] [1]A vector space over a field F is a non-empty set V together with a binary operation and a binary function that satisfy the eight axioms listed below.
In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular ordered basis. [1]
Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints).