Karim BELABAS on Tue, 30 Sep 2003 18:20:08 +0200 (MEST)

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Re: matadjoint

On Tue, 30 Sep 2003, Denis Simon wrote:
> I was wondering about the terminology 'matadjoint' used in gp. In some
> linear algebra book, I found that the 'adjoint' of a matrix is the
> transpose of the conjugate (complex conjugate) of a matrix. It seems that
> the result of matajoint is the transpose of the 'comatrix'. In which book
> can I find the name 'adjoint' for this matrix ? Is the french terminology
> different from the english one ?

cf Bourbaki (Algebre III, p199, ex 9 in my edition),
   Mehta (Matrix Theory, Section 3.2),
   Stewart (Introduction to matrix computations, Appendix 2),

The terminology is unfortunate [ nothing to do with adjoint operators in
Hilbert spaces, corresponding to your other definition, and which is even
more standard! ], but nonetheless standard. From a cursory check in our
library, this usage doesn't seem to be linked to a particular tradition.
[ although I'm ready to be corrected on that one... ]


Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425   Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://www.parigp-home.de/  [PARI/GP]