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The question is self explanatory. I just wish to know the significance of this property of matrices. Thanks

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All your variables are uncorrelated. –  J. M. May 17 '11 at 15:24
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... and it was in fact a correlation-matrix (all variables have variance 1)... –  Gottfried Helms May 17 '11 at 15:41
    
@JM Thanks very much. –  Dark Star1 May 17 '11 at 16:05
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up vote 4 down vote accepted

When the inverse covariance matrix is the identity, then the covariance matrix is the identity, which means that the entries of the random vector in question are uncorrelated and have unit variance.

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