linjärt

Linjärt is a Swedish term meaning linear, or occurring in a linear manner. In mathematics, science and engineering, the concept describes relationships, models or processes that can be described by a linear function or linear operator. A linear relation typically implies proportional change: doubling the input leads to a proportional change in the output, and the principle of superposition applies in appropriate contexts.

In basic mathematics, a linear function has the form y = mx + b, where the graph is a straight line. In higher dimensions, linear transformations are represented by matrices, mapping vectors to vectors with the property that the image of a sum is the sum of the images, and scaling a vector scales its image correspondingly. If an equation or model includes an intercept or constant term, it is often referred to as affine rather than strictly linear, though in everyday usage it may still be described as linjärt.

Linjärt is central in many fields: linear algebra studies linear objects and operations; linear regression uses linear relationships to model data; and linear systems theory analyzes circuits, mechanical systems and control processes that obey the superposition principle. In contrast, nonlinear models, where outputs do not scale proportionally with inputs or interactions occur, are described as icke-linjära.

As a linguistic note, linjärt can also function as an adverb meaning “in a linear way” or “in a straight-line manner.” The term is commonly used in Swedish technical discourse and academic writing to denote linearity or linearness.