If minor refers to determinant, then what do you call the matrix? Can I just say ‘minor determinant’ vs ‘minor matrix’

Question

Here, I ask about a proposition (stated below) and in doing so don't use the term 'minor'. What I do is when you delete row k and column $l$, you get a minor matrix. It's determinant is a minor determinant.

Proposition. Let $F$ be a field. Let $n \ge 2$ be an integer. For any $A \in F^{n \times n}$ with $rank(A)=k = n-1$, we have that some minor determinant $\det(M_{(i,j)})$ of a minor matrix of $M_{(i,j)}$, of size $k \times k$, is nonzero.

I find it weird that everywhere I've looked so far minor refers to the determinant instead of the matrix and then there's not quite a term for the matrix. What's up with this? Is it wrong/weird if I make up the terms minor matrix and minor determinant? Is there really no term for those sub-matrices you get when deleting a row and a column from a matrix?

Answer 1

Just to close off the question, here is my comment:

I think "minor matrix" is fine in this context; it's clear (at least to me) what you mean. You could also try "submatrix" maybe.

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OP's edit:

ah i think i get it: we can just say submatrix instead of 'minor matrix' because k×k submatrix out of an n×m matrix is always going to be formed out of deleting rows and columns anyway eg 2×2 submatrix of 3×3 matrix is formed if and only if you delete 1 row and 1 column so there's not necessarily a need to define 'minor matrix' from the deletion? thanks for commenting!