Construction a positive definite covariance matrix

Hi.

I am trying to simulate two seismic traces and represented as two 1D vectors. I want the correlation between and **to be a constant** i.e. 0.9 and In order to simulate these two trases I am wondering how to make this into a positive definite covariance matrix.

and is both spatially dependent, so I have introduced a gaussian correlation function and is on the form

let for j=1,2

and I though I could create a covariance matrix B where

Why is this wrong? Why is this not positive definite?

I also tried with

Which is indeed positive definite, but the simulation from this looks all wrong, and the second trace just got a super small variation around the mean compared to the first trace.

I think there is something wrong with my trail of thought here, any tip is appreciated.

Re: Construction a positive definite covariance matrix

Hey ia88.

For a valid co-variance matrix shouldn't the C in the second row be C^T (i.e. C transpose)?

Re: Construction a positive definite covariance matrix

Yes, technically, but it is symmetric so it does not matter :(

Re: Construction a positive definite covariance matrix

It will not be symmetric in general unless you use the transpose.