Vector-valued function

A function that assigns a vector to each input, often describing a path, field, or multidimensional quantity.

Function (mathematics): A relation that assigns exactly one output to each element of a specified input set. A vector-valued function is a function whose outputs belong to a vector space.
Limit of a vector-valued function: The value a vector-valued function approaches as its input approaches a specified point. Its existence is tested through the limits of component functions.
Space curve: A curve in three-dimensional space represented by a parametrized position vector. A vector-valued function traces the curve as its parameter changes.
Real-valued function: A function whose outputs are real numbers. Unlike vector-valued functions, its output at each input has a single real component.
Vector space: A set with vector addition and scalar multiplication satisfying axioms that support linear combinations. Its structure defines the kinds of outputs the function can produce.
Derivative of a vector-valued function: The limit of a vector difference quotient, describing instantaneous change with respect to the input. Differentiation gives a tangent vector or a collection of partial derivatives.
Projectile motion: The motion of an object moving under gravity after being launched, with air resistance often neglected. Position as a function of time is naturally represented by a vector.
Scalar field: A function assigning a scalar value to each point in a space. It assigns magnitudes rather than vectors to spatial inputs.
Coordinate system: A scheme that assigns numerical coordinates to points or vectors relative to chosen reference directions or basis elements. Coordinates turn vector outputs into lists of scalar functions.
Integral of a vector-valued function: The vector obtained by integrating each component of a vector-valued function. Integration accumulates vector outputs component by component.

Linked from 2 pages