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

 Messages: [ Previous | Next ]
 Dr. Eric Wingler Posts: 139 Registered: 12/12/04
Re: Complex Analysis Question
Posted: Feb 10, 2006 4:28 PM

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
> 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
>

Date Subject Author
2/8/06 junoexpress
2/8/06 Dr. Eric Wingler
2/9/06 junoexpress
2/10/06 Dr. Eric Wingler
2/12/06 junoexpress
2/13/06 Dr. Eric Wingler