Solving quadratic equations with covariance term

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Solving quadratic equations with covariance term

Stein, Luba (AIM SE)
Hi,

I would like to solve the following equation with R: Cov(A,x)=0.
A is a given matrix, x is the an unknown vector.

Is there any nice solution for this?

Thank you for your help.
Best wishes,
Luba Stein







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Re: Solving quadratic equations with covariance term

Rolf Turner

On 7/07/2009, at 2:15 AM, Stein, Luba (AIM SE) wrote:

> Hi,
>
> I would like to solve the following equation with R: Cov(A,x)=0.
> A is a given matrix, x is the an unknown vector.
>
> Is there any nice solution for this?

What on earth do you mean by ``Cov(A,x)''?  This makes no sense
at all.

        cheers,

                Rolf Turner

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Re: Solving quadratic equations with covariance term

Stein, Luba (AIM SE)
Hi,

more precisely I consider a matrix with three column vectors a_i (i=1,2,3), i.e. A=(a_1,a_2,a_3). On the other hand x should take vectors as values, i.e. x=v_j, while j goes also from 1 till 3.
Now I just want to calculate the equation Cov(a_i,x_j) = 0, where Cov(a_i,x_j) is the covariance matrix.
A is a given value and x is the variable I am looking for.

In my opinion this is an quadratic equation and makes sense.

Best wishes,
Luba





-----Urspr?ngliche Nachricht-----
Von: Rolf Turner [mailto:[hidden email]]
Gesendet: Montag, 6. Juli 2009 23:16
An: Stein, Luba (AIM SE)
Cc: [hidden email]
Betreff: Re: [R] Solving quadratic equations with covariance term


On 7/07/2009, at 2:15 AM, Stein, Luba (AIM SE) wrote:

> Hi,
>
> I would like to solve the following equation with R: Cov(A,x)=0.
> A is a given matrix, x is the an unknown vector.
>
> Is there any nice solution for this?

What on earth do you mean by ``Cov(A,x)''?  This makes no sense
at all.

        cheers,

                Rolf Turner

######################################################################
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Any views or opinions presented are solely those of the author.

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Re: Solving quadratic equations with covariance term

cberry
On Tue, 7 Jul 2009, Stein, Luba (AIM SE) wrote:

> Hi,
>
> more precisely I consider a matrix with three column vectors a_i (i=1,2,3), i.e. A=(a_1,a_2,a_3). On the other hand x should take vectors as values, i.e. x=v_j, while j goes also from 1 till 3.
> Now I just want to calculate the equation Cov(a_i,x_j) = 0, where Cov(a_i,x_j) is the covariance matrix.
> A is a given value and x is the variable I am looking for.
>
> In my opinion this is an quadratic equation and makes sense.

Well, x_j = (0,0,...,0)' will satisfy Cov( A, x_j ) = (0,...0)'.

Suggest you Google 'orthogonal complement' for nontrivial solutions.

Then peruse

  ?qr

HTH,

Chuck


p.s. Don't lose sight of FAQ 7.31

http://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f

>
> Best wishes,
> Luba
>
>
>
>
>
> -----Urspr?ngliche Nachricht-----
> Von: Rolf Turner [mailto:[hidden email]]
> Gesendet: Montag, 6. Juli 2009 23:16
> An: Stein, Luba (AIM SE)
> Cc: [hidden email]
> Betreff: Re: [R] Solving quadratic equations with covariance term
>
>
> On 7/07/2009, at 2:15 AM, Stein, Luba (AIM SE) wrote:
>
>> Hi,
>>
>> I would like to solve the following equation with R: Cov(A,x)=0.
>> A is a given matrix, x is the an unknown vector.
>>
>> Is there any nice solution for this?
>
> What on earth do you mean by ``Cov(A,x)''?  This makes no sense
> at all.
>
> cheers,
>
> Rolf Turner
>
> ######################################################################
> Attention:
> This e-mail message is privileged and confidential. If you are not the
> intended recipient please delete the message and notify the sender.
> Any views or opinions presented are solely those of the author.
>
> This e-mail has been scanned and cleared by MailMarshal
> www.marshalsoftware.com
> ######################################################################
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:[hidden email]            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901

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Re: Solving quadratic equations with covariance term

Giovanni Petris
In reply to this post by Stein, Luba (AIM SE)

It is not clear to me whether you are talking about a covariance (a
theoretical quantity depending on the distribution of A and x) or an
empirical covariance, estimated from some data.

In the first case you don't need to solve anything because, as long as
A is fixed, i.e. non-random, its covariance with anything else is
zero.

Best,
Giovanni

> Date: Tue, 07 Jul 2009 09:37:53 +0200
> From: "Stein, Luba (AIM SE)" <[hidden email]>
> Sender: [hidden email]
> Cc: "[hidden email]" <[hidden email]>
> Accept-Language: en-US, de-DE
> Precedence: list
> Thread-topic: [R] Solving quadratic equations with covariance term
> Thread-index: Acn+fxCBg0P+0HykRKGeDofFN9YatQAVYRSw
> acceptlanguage: en-US, de-DE
>
> Hi,
>
> more precisely I consider a matrix with three column vectors a_i (i=1,2,3), i.e. A=(a_1,a_2,a_3). On the other hand x should take vectors as values, i.e. x=v_j, while j goes also from 1 till 3.
> Now I just want to calculate the equation Cov(a_i,x_j) = 0, where Cov(a_i,x_j) is the covariance matrix.
> A is a given value and x is the variable I am looking for.
>
> In my opinion this is an quadratic equation and makes sense.
>
> Best wishes,
> Luba
>
>
>
>
>
> -----Urspr?ngliche Nachricht-----
> Von: Rolf Turner [mailto:[hidden email]]
> Gesendet: Montag, 6. Juli 2009 23:16
> An: Stein, Luba (AIM SE)
> Cc: [hidden email]
> Betreff: Re: [R] Solving quadratic equations with covariance term
>
>
> On 7/07/2009, at 2:15 AM, Stein, Luba (AIM SE) wrote:
>
> > Hi,
> >
> > I would like to solve the following equation with R: Cov(A,x)=0.
> > A is a given matrix, x is the an unknown vector.
> >
> > Is there any nice solution for this?
>
> What on earth do you mean by ``Cov(A,x)''?  This makes no sense
> at all.
>
> cheers,
>
> Rolf Turner
>
> ######################################################################
> Attention:
> This e-mail message is privileged and confidential. If you are not the
> intended recipient please delete the message and notify the sender.
> Any views or opinions presented are solely those of the author.
>
> This e-mail has been scanned and cleared by MailMarshal
> www.marshalsoftware.com
> ######################################################################
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>

______________________________________________
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and provide commented, minimal, self-contained, reproducible code.