[R] Solving quadratic equations with covariance term

[Charles C. Berry]

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:r.turner at auckland.ac.nz]
> Gesendet: Montag, 6. Juli 2009 23:16
> An: Stein, Luba (AIM SE)
> Cc: R-help at r-project.org
> 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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Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901