invert

Invert is a term used to describe turning something the opposite way, reversing order, position, or orientation. It appears in everyday speech as well as in scientific, mathematical, musical, linguistic, and computing contexts, where it often denotes a reversal or undoing of some kind.

In mathematics and logic, an inverse undoes another operation. The additive inverse of a number a is -a, and the multiplicative inverse is 1/a (for nonzero a). An inverse function f−1 reconstructs the input from the output of f. In linear algebra, a matrix A has an inverse A−1 if A is non-singular, such that AA−1 equals the identity matrix.

In geometry and related fields, inversion describes several ideas. Circle inversion maps points relative to a fixed center so that the product of the distances from the center to a point and its image is a constant (the square of the circle’s radius). In chemistry, Walden inversion refers to the stereochemical inversion of a chiral center, often occurring in SN2 reactions and yielding the opposite configuration.

In computer science and electronics, an inverter is a device or gate that outputs the opposite value. A NOT gate provides bitwise negation in digital circuits, and software can perform bitwise NOT to flip binary digits.

In music, inversion refers to reordering the notes of a chord so a different pitch becomes the bass note (chord inversion), or to reversing intervals within a melody (melodic inversion).

In biology and genetics, a chromosome inversion is a structural rearrangement in which a segment of a chromosome is reversed end to end, potentially altering gene order and expression.

In linguistics, inversion describes placing a component of a sentence before its usual position, such as forming questions by moving an auxiliary verb to the front.