Re: Normalize a vector ????
- To: mathgroup at smc.vnet.net
- Subject: [mg16583] Re: Normalize a vector ????
- From: "Peltio" <pelt.ioNOS at PAMiol.it>
- Date: Wed, 17 Mar 1999 23:54:58 -0500
- Organization: Peltio Inc.
- References: <7clevu$9ov@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
alessandro agresti wrote
>Let's take the complex-vector vett={1, i}
>The normalized complex-vector is {1/sqrt(2), i/sqrt(2)};
Not with the standard Dot product in R2.
You need a new definition of dot product to cope with complex components.
>in fact : Conjugate[vett].vett , we get 1.
>Now let's take the LinearAlgebra`Orthogonalization` packet and
>let's do : Normalize[vett].
>We get 1/0 infinity warning......
>why???
Because you were using the standard Dot product.
Dot[{1,I},{1,I}]
0
Here's the normalization with the right one
Normalize[{1,I},InnerProduct->(Dot[#1,Conjugate[#2]]&)]
{1/sqrt(2), I/sqrt(2)};
Kinda sure that helps.
Peltio
peltioNOS at PAMusa.net