What does the "adjoint of a matrix" mean to you?

I was brought up to understand it to mean the transpose of the matrix
of signed minors, a matrix close to being the inverse of the
original.  Poking around (Wikipedia, Planet Math, Math World) would
imply this is known as the "classical adjoint."  Hmmm, I'm not that
old.  Anyway, it is also known now as the "adjugate matrix."

It seems that the term "adjoint" is now more commonly used for the
conjugate-transpose of a matrix (and for vectors) and that's what I
find in most any relatively new textbook on matrix algebra.

Presently, in Sage, "adjoint" gives the "classical" interpretation.  I
would much prefer to define and implement the adjoint of a matrix to
be the conjugate transpose.  So two questions:

1.  Thoughts on what "adjoint" should be?

2.  If adjoint were to be redefined to a more modern interpretation,
its current use could be aliased to "adjugate" and deprecated, but
that won't make it available for reuse until the deprecation period
runs its course.  Any precedent, or techniques, for radically
redefining a method name?

Rob

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