liniowych

Liniowych is a Polish adjective form derived from liniowy and used to describe things that have a linear or line-like character. In Polish scientific and technical writing it appears as a modifier for plural nouns, for example in phrases such as układów liniowych równań or modele liniowe, indicating that the objects or models are linear.

In mathematics and related disciplines, the term is common with nouns like równania, funkcje, przekształcenia and układy. Równania liniowe are equations whose terms involve at most first powers of the variables; funkcje liniowe are functions with a constant rate of change; przekształcenia liniowe are linear transformations that preserve addition and scalar multiplication; układy liniowych równań are systems of linear equations. Liniowość implies additivity and proportionality, meaning operations can be represented by linear expressions.

In statistics and data analysis, the phrase modele liniowe refers to models in which the expected value of the dependent variable is a linear function of the parameters. Regresja liniowa is a common method within this class, providing straightforward estimation and interpretation. Liniowe approaches are typically contrasted with nonlinear models when simple interpretation and closed-form solutions are priorities.

Beyond mathematics, the term appears in engineering, physics and computer science to describe linear approximations, linear methods, or linear algebra topics such as przekształcenia liniowe used in signal processing and graphics. The root of the word lies in linia, meaning line, itself derived from Latin line-a, reflecting the historical association with straight-line relationships.