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Topic: Complex Analysis Question
Replies: 5   Last Post: Feb 13, 2006 1:59 PM

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Dr. Eric Wingler

Posts: 139
Registered: 12/12/04
Re: Complex Analysis Question
Posted: Feb 10, 2006 4:28 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

It would be helpful if you quoted the original question along with my
response.

The solutions to z' * x = 0 form a linear subspace of C^n.


________________________________
Eric J. Wingler (wingler@math.ysu.edu)
Dept. of Mathematics and Statistics
Youngstown State University
One University Plaza
Youngstown, OH 44555-0001
330-941-1817



"junoexpress" <mathimagical@netscape.net> wrote in message
news:1139536604.969390.253390@f14g2000cwb.googlegroups.com...
> I'm not sure there is much I can make out of this.
>
> The problem I am having using the fact you provided is that it is not
> obvious to me what it implies in Cn.
> Essentially, z has 2n free parameters and the eqns
> (i.a) z' * x = 1
> (i.b) z' * x = 0 i
> gives me constraints on 2 of the params.
>
> Doing the subtraction you suggested essentially tells me that the 2n
> params in z1 - z2 solve two homogeneous linear equations, which still
> means that there are 2n-2 free params.
>
> So it seems that an algebraic approach is not going to get me anywhere.
> Geometrically, I am not sure what z' * x = 0 means. If the vectors were
> in Rn, I would know that z'*x=0 means that they are orthogonal, but I
> am not sure that this is even what z'*x=0 means in Cn.
>
> Juno
>






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