Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Able to be inverted, having an inverse.
from the GNU version of the Collaborative International Dictionary of English
 adj. Capable of being inverted or turned inside out.
 adj. Capable of being changed or converted.
 adj. Incapable of being turned or changed.
from The Century Dictionary and Cyclopedia
 Capable of inversion; susceptible of being inverted.
 Incapable of being turned; inflexible.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. having an additive or multiplicative inverse
Etymologies
Examples

Ketonen's bestknown discovery is a sequent calculus for classical propositional logic the logical rules of which are all invertible, meaning that whenever a sequent is of a form that matches the conclusion of a logical rule, the corresponding premisses, defined uniquely from the given sequent and the rule, are also derivable.

Since the transformation is invertible, the essential fact is that any property of the first structure will have a correlated property in the second; and any property of the second will have a correlated property in the first.

Not sure where I read, either, that the use of the term “linear” should not be confused with linear transformation a trend is not invertible, though the line it creates is… maybe it was at the wiki site?

In particular, in order to use tree ring proxies for temperature reconstruction, it is necessary to show that the growth function for the selected tree proxies is invertible, or that the limitation of the nonlinear response curve can be addressed in some other manner.

Wrote cryptology formula finding the number of invertible matrices in Hill cipher.

The word for The Da Vinci Code is a rare invertible palindrome.
The Da Vinci Code: Summary and book reviews of The Da Vinci Code by Dan Brown.

Spinner is a highly durable, invertible, 6WD vehicle that responds to the need of a UGCV to surmount challenging terrain obstacles, be easily teleoperated, and withstand an occasional moderate crash and rapidly recover.

In general, an automorphism of a space, any space, is an invertible transformation of the entire space into itself, and such a transformation is nothing other than a rearrangement of the totality of the points of the space from their given ordering into any other.

The three elementary row operations used in the Gaussian elimination (multiplying rows, switching rows, and adding multiples of rows to other rows) amount to multiplying the original matrix with invertible matrices from the left.

The first part of the algorithm computes an LU decomposition, while the second part writes the original matrix as the product of a uniquely determined invertible matrix and a uniquely determined reduced rowechelon matrix.
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