lineárne

Lineárne is a Slovak adjective meaning "linear" and is used to describe things related to a line or to linearity. In mathematics, lineárny denotes a property that can be described by straight-line relationships or by additivity and homogeneity. A linear function satisfies f(x+y)=f(x)+f(y) and f(c x)=c f(x). A linear transformation T between vector spaces preserves addition and scalar multiplication: T(u+v)=T(u)+T(v) and T(cu)=cT(u). A linear equation has the form a1x1+...+anxn=b and represents a hyperplane in n-dimensional space. A linear space, or vector space, is a set with well-defined addition and scalar multiplication that satisfy the usual axioms. Concepts such as linear independence, linear combinations, and basis are fundamental in linear algebra.

In applied contexts, linearity underpins several methods and models. Linear programming optimizes a linear objective subject to linear constraints. Linear regression models predict a response as a linear function of explanatory variables. In algorithms, linear time means running time grows proportionally with input size. In calculus, linear approximation uses the tangent line to approximate a function near a point. A related concept is affine linearity, where a function has the form f(x)=Ax+b; such mappings are affine but not linear in the strict sense. In ordinary language, lineárne can describe straightforward, proportional relationships that resemble a straight-line relation.

The term lineárne derives from Latin linearis via the idea of a line, and in Slovak the base adjective is lineárny, with lineárne serving as the neuter or predicative/attributive form in phrases describing objects or concepts.