[petsc-dev] various dot products messed up for complex numbers?

[Barry Smith]

  Sure it is and arbitrary convention that isn't universal.

   My original email comment "real mathematicians" was just a wise-crack 

    Barry

On Apr 15, 2012, at 1:49 PM, Jed Brown wrote:

> On Sun, Apr 15, 2012 at 13:32, Barry Smith <bsmith at mcs.anl.gov> wrote:
> (ax,y)  = a(x,y)
> 
> This is an arbitrary convention that isn't universal. You occasionally see a(x,y) = (x,Ay). You certainly see <x|H|y> which is equal to <x|H y>. I like to write things like
> 
> v^H J(u) w \sim J[u](v,w) = (v,J[u] w) = \int_\Omega v^* \cdot J(u) w
> 
> where the left side of the \sim is discrete with v,u,w vectors and J(u) the Jacobian; and versions to the right are all continuous (with J[u] an operator and J(u) the tensor-valued field).
> 
> If I had to use that screwy inner product notation, this would become
> 
> v^H J(u) w \sim J[u](w,v) = (J[u] w,v) = \int_\Omega v^* \cdot J(u) w
> 
> which is needlessly error-prone.