"minor" typo: docs globally (?) misuse the term "minor"

[jaganmn]

I am not aware of a text that defines a minor to be a matrix. Hence I was bit surprised to read

the leading minor of order i is not positive definite

here:

lapack/SRC/dpotrf.f

Lines 87 to 92 in cea4a63

	*> INFO is INTEGER
	*> = 0: successful exit
	*> < 0: if INFO = -i, the i-th argument had an illegal value
	*> > 0: if INFO = i, the leading minor of order i is not
	*> positive definite, and the factorization could not be
	*> completed.

Actually, grep -n SRC/*.f -e "minor" reveals many more instances ...

AFAIK, a minor is a determinant and not a matrix (see, e.g., Aitken, 1944, p. 39; Horn and Johnson, 2013, p. 17; ...), and it is therefore nonsense to consider whether a minor is positive definite. Should the text be globally amended to

the leading principal minor of order i is not positive

or

the leading principal submatrix of order i is not positive definite

depending on context? It would be the former in the case of DPOTRF, at least according to Sylvester's criterion ...

• I've included a minimal example to reproduce the issue
• I'd be willing to make a PR to solve this issue

[langou]

I agree. A PR would be welcome.

[martin-frbg]

would it make sense to add a label "documentation bug" for such cases ? "bug" by itself suggests (to me) a serious coding error and unexpected results, not an English math semantics issue with the documentation.

[jaganmn]

I've created a PR with #849 - surprisingly to me it has not been automatically linked here ... Anyway, I agree that a "documentation" tag would have made sense in this case.

[weslleyspereira]

would it make sense to add a label "documentation bug" for such cases ? "bug" by itself suggests (to me) a serious coding error and unexpected results, not an English math semantics issue with the documentation.

We could do that. Or maybe just use the label "Related: Documentation" in addition to (or even instead of) "Type: Bug". I don't have a strong opinion on that.

[langou]

I added the label Related: Documentation and I removed the label Type: Bug.