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

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

Eric J. Wingler (
Dept. of Mathematics and Statistics
Youngstown State University
One University Plaza
Youngstown, OH 44555-0001

"junoexpress" <> 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

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