# [Numpy-discussion] adding two pseudoinverse matrixes

Jose Borreguero borreguero@gmail....
Fri Sep 10 16:11:51 CDT 2010

```Thanks for your suggestion, Chuck. The equation arises in the substraction
of two harmonic potentials V and V':
V' = 1/2 x^t  * A^(-1)  * x
V= 1/2 x^t  * B^(-1) * x
V'-V = 1/2 x^t * ( A^(-1) - B^(-1) ) * x = 1/2 x^t  * Z^(-1) * x

A is the covariance matrix of the coordinates x in a molecular dynamics
simulation, A = <x * x^t >. Same goes for B.

-Jose

On Fri, Sep 10, 2010 at 5:02 PM, Charles R Harris <charlesr.harris@gmail.com
> wrote:

>
>
> On Fri, Sep 10, 2010 at 2:39 PM, Jose Borreguero <borreguero@gmail.com>wrote:
>
>> Dear Numpy users,
>>
>> I have to solve for Z in the following equation Z^(-1) = A^(-1) - B^(-1),
>> where A and B are covariance matrices with zero determinant.
>>
>> I have never used pseudoinverse matrixes, could anybody please point to me
>> any cautions I have to take when solving this equation for Z? The brute
>> force approach linalg.pinv( linalg.pinv(A) - lingal.pinv(B) ) gives me a
>> matrix with all entries equal to 'infinity'.
>>
>>
> Similar sorts of equations turn up in Kalman filters. You can also try
> tricks like  Z = B * (B - A)^-1 * A . Where does this problem come from?
> There might be a better formulation.
>
> Chuck
>
>
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