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What is invertibility?

What is invertibility? Here are some definitions.

Noun
  1. (mathematics) The condition of being invertible.
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Examples
The key challenge is to appropriately exploit these scores, their survey of multiple features per position, their underlying group structure, and their invertibility.
An invertibility requirement, whereby the moving average equation can be recast into an autoregressive form also constrains the moving average parameters.
Two methods of studying the invertibility of operators belonging to the above-mentioned algebras are described.
The invertibility of this process requires that the endogenous variables in the VAR should not be integrated.
Coefficients of the ARMA models are also checked for both stationarity and invertibility.
This captures an idea that Callander refers to as proportional invertibility.

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