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Determinant of auto correlation matrix

  1. Sep 8, 2011 #1
    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.
     
  2. jcsd
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