In my math textbook, I saw an author use “square and invertible matrix.” Which one is more correct: “invertible square matrix” or “invertibly square matrix”?

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    Ask a mathematician. Specialized language like that is decided by the people who use it regularly, not by grammarians or linguists. Mar 1, 2020 at 18:03
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    Invertible square matrix. It's a square matrix that's invertible, not a matrix that's 'square in an invertible way' (which would make no sense). As John L well knows. Though his 'comment' is really the more appropriate. Mar 1, 2020 at 19:31
  • If you solve a square matrix problem involving inversion, you will know which phrase to use. So I'd suggest that you go solve a matrix problem.
    – Mr. X
    Mar 1, 2020 at 20:06
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    I'm voting to close this question as off-topic because it belongs on Mathematics with the terminology tag.
    – CJ Dennis
    Mar 1, 2020 at 21:25
  • My LA is a little rusty, but Nicholas' answer is correct. Also, @CJDennis, I disagree with closing; while this does deal with a math term, I think understanding why "invertible" is correct and "invertibly" is not is on topic. BTW, also, "invertible square" is redundant; only square matrices can be invertible.
    – Matthew
    Mar 2, 2020 at 4:07

1 Answer 1


With my limited knowledge on Linear Algebra, I view it as such:

invertible square matrix

This means your matrix is both square and invertible. It has an order of n*m where n equals m, and it is also invertible.

invertibly square matrix

This implies that your matrix is square, and how square is it? It is invertibly square. I do not know if that even makes sense to say that something is invertibly square. Something can be almost square or perfectly square or permanently square, but I don't see how invertibly square could possibly mean anything.

Thus, I would say that using an adjective here probably means what you intended to mean.

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