#10501: Deprecate adjoint in favor of adjugate
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Reporter: rbeezer | Owner: jason, was
Type: task | Status: needs_work
Priority: major | Milestone: sage-4.6.2
Component: linear algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by tornaria):
* status: needs_review => needs_work
Comment:
I already stated some objections to this on the mailing list, but I'll
repeat:
On deprecating "adjoint" meaning "matrix of cofactors"
1. it's standard terminology and has meant this in sage for long
2. "adjugate" is newer and (IMO) less standard terminology -- in
particular it has no obvious translations
On using "adjoint" meaning "conjugate transpose"
3. "conjugate transpose" is easy to say, and it's really what is meant
4. the "adjoint operator" for a matrix seems ill-defined, because a
matrix is not an operator but only a representation of an operator in some
basis.
Moreover, if there are two colliding usages of the name "adjoint", I would
find it more reasonable to keep the usage that is already traditional in
Sage.
The usage of "adjoint" is ubiquitous in relation to quadratic forms afaict
(and, as John Cremona pointed out, is where the term originates with Gauss
on ternary quadratic forms)
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Reference for "Adjoint of a matrix":
Bourbaki, Elements, book 2, chapter III, section 11, exercise 9:
The adjoint of a square matrix X of order n over A is the matrix X =
(det (A'")) of minors of A" of order n — 1.
(Note that the term also shows at the index of terminology of the book)
PS: searching for
"The adjoint of a square matrix" bourbaki
in books.google.com, yields the above passage.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10501#comment:2>
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