underbestämd

Underbestämd is a Swedish term that translates to "underdetermined" in English. It is most commonly used in mathematics and engineering to describe a system with fewer independent equations than variables. When a system is underdetermined, it means there is not enough information to find a unique solution. Instead, there are infinitely many possible solutions.

In the context of linear algebra, an underdetermined system of linear equations has more variables than equations. This leads to a situation where the solution space has at least one degree of freedom. Geometrically, this often translates to lines or planes that extend indefinitely, allowing for an infinite number of points that satisfy all the equations simultaneously.

The concept of underdetermined systems is important in various fields. For instance, in image reconstruction or signal processing, an underdetermined system might arise when trying to reconstruct a signal from incomplete or noisy data. In such cases, techniques like regularization are employed to find a plausible or "best" solution among the infinite possibilities, often by introducing prior knowledge or constraints. It is the opposite of an overdetermined system, which has more equations than variables and may have no solution or a unique solution if the equations are consistent.