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In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar ...
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, 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 ...
Vector field. A portion of the vector field (sin y , sin x) In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space . [ 1] A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane.
Vector (molecular biology) In molecular cloning, a vector is any particle (e.g., plasmids, cosmids, Lambda phages) used as a vehicle to artificially carry a foreign nucleic sequence – usually DNA – into another cell, where it can be replicated and/or expressed. [ 1] A vector containing foreign DNA is termed recombinant DNA.
Euclidean vector. 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. Euclidean vectors can be added and scaled to form a vector space. A Euclidean vector is frequently represented by a ...
v. t. e. Kinematics is a subfield of physics and mathematics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. [ 1][ 2][ 3] Kinematics, as a field of study, is often referred to as the "geometry of motion ...
Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as points, lines, curves and polygons. The associated mechanisms may include vector display and printing hardware, vector data models and file formats, as well as the software based on these data ...
Vector space. Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2w. In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and ...
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