niezerowych

Niezerowy is a Polish adjective meaning nonzero, used in mathematics to describe elements that are not equal to zero. The term appears in many standard phrases, such as liczb niezerowych (nonzero numbers), wektorów niezerowych (nonzero vectors), and elementów niezerowych (nonzero elements). It serves to distinguish quantities, vectors, or elements from the zero element in a given set or structure.

Grammar and usage notes: niezerowy declines like other Polish adjectives. In plural phrases, several forms appear depending on case and number. The form niezerowych is the genitive plural (and can be found in phrases like elementów niezerowych or wartości niezerowych), while niezerowe is used in the nominative plural when describing feminine nouns such as liczby niezerowe. The base compound distinguishes zero from nonzero across contexts, including linear algebra, number theory, and set theory.

Contexts and examples: In linear algebra, key concepts include niezerowy wektor (a nonzero vector) and niezerowy wektor własny (a nonzero eigenvector). In number theory and arithmetic, one often refers to niezerowe liczby całkowite (nonzero integers) or niezerowe wartości pewnych funkcji. The distinction between zero and nonzero is fundamental for defining solutions to equations, determinants, ranks, and other structural properties.

See also: Zero (mathematics), Nonzero element, Zero divisor, Eigenvector. The term niezerowych is a declined form used within noun phrases to express “of nonzero” elements, emphasizing the property of being different from zero.