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Vector-valued function. 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 ...
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 fields are often used to model, for example, the speed ...
Connected Home over IP (or Project Connected Home over IP) is an open-sourced, royalty-free home automation connectivity standard project which features compatibility among different smart home and Internet of things (IoT) products and software
Python uses the + operator for string concatenation. Python uses the * operator for duplicating a string a specified number of times. The @ infix operator. It is intended to be used by libraries such as NumPy for matrix multiplication. The syntax :=, called the "walrus operator", was introduced in Python 3.8. It assigns values to variables as ...
In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator that assigns to any two vector fields X and Y on a smooth manifold M a third vector field denoted [X, Y] . Conceptually, the Lie bracket [X, Y] is the derivative of Y ...
Solenoidal vector field. An example of a solenoidal vector field, In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field) is a vector field v with divergence zero at all points in the field: A common way of expressing this property is to say that ...
In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose gradient is a given vector field. Formally, given a vector field v, a vector potential is a vector field A such that.
Vector operators include the gradient, divergence, and curl: Gradient is a vector operator that operates on a scalar field, producing a vector field. Divergence is a vector operator that operates on a vector field, producing a scalar field. Curl is a vector operator that operates on a vector field, producing a vector field. Defined in terms of del: