Bill Allombert on Wed, 1 Oct 2003 12:34:31 +0200

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Re: matadjoint

On Tue, Sep 30, 2003 at 11:17:29AM +0200, Denis Simon wrote:
> Hello dear pari-dev,
> 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 ?

In the french terminology the 'matrice ajointe' is the 
transpose of the comatrix.

This is not the same as the matrix of the "operateur adjoint"
of an operator which is defined by <Ax,y>=<x,A^*y>.
If the scalar product is the canonical euclidean scalar product, A^*=A^t. 
If it is the canonical hermitian scalar product, A^*=conj(A^t).
Note that the above formula only stand for orthogonal basis.