conjugado

Conjugado is the Spanish term for conjugate or conjugated, used across disciplines to denote a related partner, a transformed form, or an associated mathematical object. The word comes from Latin conjugatus and appears in various technical contexts with related but distinct meanings.

In grammar, conjugado refers to a verb form that has been inflected to express person, number, tense, mood, aspect, and voice. A forma conjugada contrasts with the infinitive, gerund, or participle, reflecting the verb’s agreement with a subject or grammatical category in a sentence.

In mathematics and related fields, conjugado covers several notions. The complex conjugate of z = a + bi is z̄ = a − bi; their product z z̄ equals a^2 + b^2, a real number. The conjugate transpose, denoted A* or A^H, is the transpose of a matrix with each entry replaced by its complex conjugate. In group theory, the conjugate of an element a by g is g^−1 a g. For quaternions, the conjugate q̄ = a − bi − cj − dk reverses the imaginary components.

In chemistry, conjugado describes a system with alternating single and multiple bonds that allows delocalization of π electrons, forming a conjugated system. Such delocalization influences properties like color, stability, and reactivity, with benzene and polyenes as prominent examples.