conjugált

Conjugált (conjugated) is a term used in several disciplines to describe entities related by a conjugation operation or by belonging to a conjugate pair. In linguistics, a verb is conjugated to reflect grammatical categories such as person, number, tense, mood, voice, and aspect. Conjugated forms vary between languages and are governed by rules of grammar; they enable speakers to express who does the action and when it occurs.

In mathematics, conjugation commonly refers to the complex conjugate. The complex conjugate of z = a + bi is z̄ = a − bi. The product z z̄ equals a^2 + b^2 = |z|^2, and conjugation is an involution (applying it twice yields the original number). In group theory, two elements are conjugate if one can be transformed into the other by a change of basis within the group: x and g x g^-1 lie in the same conjugacy class.

In chemistry, conjugation denotes systems with alternating single and multiple bonds, enabling delocalization of pi electrons across adjacent atoms. Conjugated systems exhibit distinctive electronic, spectroscopic, and stabilizing properties, and are central to many dyes, pigments, and aromatic compounds.

In numerical analysis, the term appears in algorithms such as the conjugate gradient method, which uses conjugate directions to solve large symmetric positive-definite linear systems efficiently.

Conjugation thus spans linguistics, algebra, analysis, chemistry, and numerical methods, reflecting a common idea of a linked, reciprocal relationship between entities.