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A graph of the vector-valued function r(z) = 2 cos z, 4 sin z, z indicating a range of solutions and the vector when evaluated near z = 19.5. A common example of a vector-valued function is one that depends on a single real parameter t, often representing time, producing a vector v(t) as the result.
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.
An operator is a function over a space of physical states onto another space of states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context).
The four-dimensional system of quaternions was discovered by W.R. Hamilton in 1843. [6] The term vector was introduced as v = xi + yj + zk representing a point in space. The quaternion difference p – q also produces a segment equipollent to pq. Other hypercomplex number systems also used the idea of a linear space with a basis.
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings.
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; H is the magnetic field's auxiliary field vector or magnetizing field.
Computer model of the Vector-06C. Vector-06C was created by Soviet engineers Donat Temirazov and Alexander Sokolov from Kishinev, Moldovan SSR.On 33rd National Radio Exhibition the design was honoured with the grand prize.