inversies

Inversions, or inversies, refer to processes or operations that produce a reversal of order, direction, or value. The term is used across disciplines to describe how one element becomes its opposite or sits in a reversed position relative to another.

In mathematics, an inverse operation undoes another: the additive inverse is negation, the multiplicative inverse is reciprocal. A function has an inverse if it is bijective, yielding an inverse function f^-1; a square matrix has an inverse only if its determinant is nonzero.

In geometry, inversion with respect to a circle maps a point to a new location along the same ray from a chosen center, with the distance from the center inversely related to the original distance; it is a classical conformal transformation.

In linguistics, inversion is a reversal of normal word order, often used in questions or for emphasis, as in “Never have I seen such a scene.”

In music, inversion refers to reordering the notes of a chord so a different note serves as the bass; common forms include the first and second inversions, and melodic inversion flips interval directions.

In biology, an inversion is a chromosome rearrangement in which a segment is reversed end to end, which can affect gene expression and recombination.

In physics, inversion relates to parity or spatial inversion, a symmetry operation that flips coordinates to test invariance.