If a matrix has the same number of rows and columns, we call it a square matrix. The analogous concept for linear operators would be operators with the same domain and range, i.e., endomorphisms.

Is there an **established** adjective that can be added to the word "operator" that denotes this concept?

In other words, what could I fill in for *xxx* in the following example sentence: "A square matrix is invertible iff it has full rank, but not every full-rank *xxx* operator is invertible."

**Note:** In many texts, "operator" already implies that domain and range are the same, but in some texts this is not assumed. Often, this distinction is left implicit. For example, "A course in functional analysis" (Conway 1990) considers bounded operators with different domain and range, while in what is basically the follow up book "A course in operator theory" (Conway 2000), bounded operators are assumed to have same domain and range.

**Short summary of suggestions**

- Endomorphic operator (this comment)
- Endo-operator or "... is endo" (this answer)
- Square operator (Textbook: The Theory of Quantum Information, John Watrous)

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