# Determinant of auto correlation matrix

1. Sep 8, 2011

### vaibhavtewari

Hello everyone, I have a question..

if I have a data stream
X=some thousand random numbers with mean close to 0 and standard deviation close to 1 and then I construct my autocorrelation matrix from these numbers

Q=|R_xx{0} R_xx{1}.........R_xx{L}|
| R_xx{1} R_xx{0} ......R_xx{L-1}|
|...............................................|
|R_xx{L}........................R_xx{0}|

I normalize the matrix(getting 1 on diagonal) and calculate its determinant. As I am using a gaussian random number distribution for x, in theory I would get 0 for off-diagonal terms and 1 for diagonal terms. But in reality I have 1 on diagonal(because of normalization) and very small numbers for off-diagonal. The determinant turns out to be less than 1. Also the determinant is dependent on L, for small L its close to 1, as I increase L determinant starts decreasing. My question is is there a way I can normalize the determinant of this matrix so that I always get 1 for uncorrelated data ?

Thank You for reading this long description.