vektorväärtuslikud

Vektorväärtuslikud is a Finnish term that translates to "vector-valued" in English. It describes a mathematical function or object whose output is a vector. In contrast to scalar-valued functions, which produce a single numerical value, vector-valued functions produce a list or array of numbers, where each number represents a component of the resulting vector.

These types of functions are fundamental in various fields of mathematics and physics. For instance, in multivariable calculus, a function mapping from a subset of R^n to R^m is a vector-valued function. An example is a function describing the position of a particle in three-dimensional space over time, where the input is time (a scalar) and the output is a vector (x, y, z) representing the particle's coordinates.

Vector-valued functions are crucial for describing physical quantities that have both magnitude and direction, such as velocity, force, or electric fields. They are used extensively in areas like differential geometry, where they define curves and surfaces, and in physics, for modeling complex systems. The concept extends to higher dimensions and more abstract vector spaces, forming a cornerstone of modern mathematical analysis and its applications.