inversible

Inversible is an adjective meaning capable of being inverted or reversed. Its etymology traces to the Latin inversus, meaning turned inward or upside down, combined with the suffix -ible. In English, the term invertible is far more common; inversible is relatively rare and is often encountered in older texts, in translations, or in specific technical contexts.

In mathematics and related fields, inversible is typically superseded by invertible. A function is invertible if there exists a two-sided inverse function, which occurs precisely when the function is bijective. A square matrix is inversible when it has an inverse, which is equivalent to having a nonzero determinant. In common usage, “invertible” is the standard term in linear algebra, calculus, and many areas of computer science.

The distinction among related terms centers on nuance. Invertible emphasizes the existence of an exact inverse operation or mapping. Reversible, by contrast, denotes the ability to undo a process, potentially without guaranteeing a unique inverse. Inversible sits between these concepts and is most often encountered in linguistic or cross-linguistic usage, or as a stylistic variant in technical writing where compatibility with other Romance-language terms is desired.

Usage notes and style guidance suggest using invertible in modern English mathematical writing. Inversible may appear in historical documents, in multilingual texts, or when translating from languages where the equivalent term is standard. When clarity is essential, prefer invertible for mathematical objects and reversible for processes or procedures.