Inversion

Inversion is a general term for reversal of position, order, orientation, or relationships within a system. It is used across disciplines to describe changes that produce the opposite of a given arrangement, often with field-specific terminology and rules.

In linguistics, inversion refers to a reversal of typical word order. Subject-auxiliary inversion occurs in questions, as in "Are you coming?" Inversion can also appear after negative adverbials or in certain copular constructions, often signaling emphasis or formality.

In mathematics and logic, inversion denotes several related ideas. An inverse function undoes a function, exchanging inputs and outputs: f^-1(y) gives x where f(x) = y. The multiplicative inverse of a nonzero x is 1/x. A matrix is invertible when its determinant is nonzero, yielding a unique inverse matrix. Inversion also appears in various algebraic and relational structures.

In music theory, inversion rearranges the notes of a chord or interval so a different pitch forms the bass. For triads, the first inversion places the third in the bass, the second inversion the fifth. Inversion changes voicing and harmonic texture without altering the chord’s pitch content.

In meteorology, a temperature inversion describes a layer where temperature increases with altitude, contrary to the usual decrease. Inversions can trap pollutants, affect fog and cloud formation, and influence weather stability, particularly in valleys or stable air masses.

In genetics, a chromosomal inversion reverses the orientation of a segment within a chromosome. Pericentric inversions include the centromere; paracentric inversions do not. Inversions can influence recombination and evolutionary trajectories. In anatomy, inversion also denotes turning the sole inward at the foot, contrasted with eversion.