how to reduce covariance matrix

[Förster vom Silberwald]

Hello:

Probably basic silly question. However, given a 50 times 50 covariance
matrix.

Is it possible to create a 4 times 4 covariance matrix out of it
(nothing further given than just the 50x50 covariance).

Thanks

[Ray Koopman]

On Nov 30, 11:35 am, "Förster vom Silberwald" <chain_l...@hotmail.com>
wrote:

There are an infinite number of ways to do it.
What are you (or they) trying to accomplish?

[Förster vom Silberwald]

I have a 67x67 covariance matrix from observations (pressure level
related: 67 pressure levels in number). For my inversion to work I
just need 3 pressure regimes. Or better said my Jacobian is somehow of
that dimension. That is the reason why I asked if it is possible to
'reduce' the 67x67 to something like 3x3.

I lack somewhat the terminology and it is hard to find some methods
how to do it. My first approach would have been to calculate the
average in the 3x3 grid boxes of the larger finer grid boxes 67x67.
But not sure on this.

Thanks you very much for any further insights or pointer to methods

[Art Kendall]

I am not sure I understand your question.

If you have a square covariance matrix with the same labels on the row
and column stubs, you could do some form of factor analysis like
principal components and represent the 67 dimensional space in the three
dimensional space that accounts for as much of the total variance as
possible.

The most common kind of covariance used in factor analysis is the
covariance(correlation) of a number of variable with each other found
from a larger number of cases.

Art Kendall
Social Research Consultants

[Ray Koopman]

On Nov 30, 12:15 pm, "Förster vom Silberwald" <chain_l...@hotmail.com>

If you want to work with the averages over certain ranges of pressure
levels then you can partition the covariance matrix accordingly and
use the average within each block.