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Thread Subject:
vectors in subspace

Subject: vectors in subspace

From: Frank

Date: 15 Dec, 2010 02:44:06

Message: 1 of 6

I have a question about vectors in a K times (K-1) subspace.

I would like to generate a K by 1 complex vector with structure z = [1, a_2, a_3, ..., a_K]^T where a_2, a3,...,a_K are all with magnitude 1, that is, a_n = exp(1i*w_n) and the 'n' in w_n is is the subscript.

How many different z can I generate where all of them lies in a subspace with dimension K times (K-1)?

Can anyone help?

Thanks a lot.

Frank

Subject: vectors in subspace

From: Rune Allnor

Date: 15 Dec, 2010 05:07:23

Message: 2 of 6

On Dec 15, 3:44 am, "Frank " <allinone_2...@yahoo.com.hk> wrote:
> I have a question about vectors in a K times (K-1) subspace.
>
> I would like to generate a K by 1 complex vector with structure z = [1, a_2, a_3, ..., a_K]^T where a_2, a3,...,a_K are all with magnitude 1, that is, a_n = exp(1i*w_n) and the 'n' in w_n is is the subscript.
>
> How many different z can I generate where all of them lies in a subspace with dimension K times (K-1)?

Homework?

Rune

Subject: vectors in subspace

From: Frank

Date: 15 Dec, 2010 07:28:05

Message: 3 of 6

No, can anyone help?

Thanks.

Rune Allnor <allnor@tele.ntnu.no> wrote in message <b3ea67a3-aa22-46c1-993f-08a90a5c5394@y31g2000vbt.googlegroups.com>...
> On Dec 15, 3:44 am, "Frank " <allinone_2...@yahoo.com.hk> wrote:
> > I have a question about vectors in a K times (K-1) subspace.
> >
> > I would like to generate a K by 1 complex vector with structure z = [1, a_2, a_3, ..., a_K]^T where a_2, a3,...,a_K are all with magnitude 1, that is, a_n = exp(1i*w_n) and the 'n' in w_n is is the subscript.
> >
> > How many different z can I generate where all of them lies in a subspace with dimension K times (K-1)?
>
> Homework?
>
> Rune

Subject: vectors in subspace

From: Bruno Luong

Date: 15 Dec, 2010 07:40:23

Message: 4 of 6

"Frank " <allinone_2003@yahoo.com.hk> wrote in message <ie9a1m$rn7$1@fred.mathworks.com>...
> I have a question about vectors in a K times (K-1) subspace.
>
> I would like to generate a K by 1 complex vector with structure z = [1, a_2, a_3, ..., a_K]^T where a_2, a3,...,a_K are all with magnitude 1, that is, a_n = exp(1i*w_n) and the 'n' in w_n is is the subscript.
>
> How many different z can I generate where all of them lies in a subspace with dimension K times (K-1)?

Hnt: make a connection with Discrete Fourier Transform (DFT) matrix.

Bruno

Subject: vectors in subspace

From: Frank

Date: 16 Dec, 2010 02:07:05

Message: 5 of 6

Do you mean that there are K vectors I can generate?

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <ie9rd6$bbs$1@fred.mathworks.com>...
> "Frank " <allinone_2003@yahoo.com.hk> wrote in message <ie9a1m$rn7$1@fred.mathworks.com>...
> > I have a question about vectors in a K times (K-1) subspace.
> >
> > I would like to generate a K by 1 complex vector with structure z = [1, a_2, a_3, ..., a_K]^T where a_2, a3,...,a_K are all with magnitude 1, that is, a_n = exp(1i*w_n) and the 'n' in w_n is is the subscript.
> >
> > How many different z can I generate where all of them lies in a subspace with dimension K times (K-1)?
>
> Hnt: make a connection with Discrete Fourier Transform (DFT) matrix.
>
> Bruno

Subject: vectors in subspace

From: Bruno Luong

Date: 16 Dec, 2010 08:11:05

Message: 6 of 6

"Frank " <allinone_2003@yahoo.com.hk> wrote in message <iebs89$qlh$1@fred.mathworks.com>...
> Do you mean that there are K vectors I can generate?
>

I don't mean anything but providing the hint, since I don't know understand what is
"subspace with dimension K times (K-1)".

This is not the standard definition I have learn in Math school.

Bruno

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