linearni

Linearni is an adjective meaning "linear" in several South Slavic languages, including Croatian, Bosnian, Serbian, and Slovenian. It derives from Latin linearis, via the older Slavic term for line, and is used in mathematics, science, and everyday language to describe properties that relate to a straight line or a first-degree relationship.

In mathematics, "linear" denotes properties preserving addition and scalar multiplication. The central concepts include linear functions or maps, linear equations, linear systems, linear independence, and linear combinations. A linear map L satisfies L(u+v) = L(u) + L(v) and L(cu) = c L(u) for all vectors u, v and scalars c.

In statistics and data analysis, "linearni model" and "linearna regresija" are common terms for models in which the expected value is a linear function of the parameters. In geometry and physics, the term often describes entities that lie on a line or relationships that are proportional and additive.

Usage extends to everyday language as well, where linear relationships describe proportional, straight-line behavior or processes that can be approximated by first-order relations. In scientific and engineering contexts, the concept of linearity underpins many models and analyses, including linear time-invariant systems and linear approximations.

See also: linearity, line, linear algebra, linear regression.