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Assume that all the entries of an $n \times n$ correlation matrix which are not on the main diagonal are equal to $q$. Find upper and lower bounds on the possible values of $q$.

I know that the matrix should be positive semidefinite but how to proceed to get the upper and lower bounds?

Thanks!

  • 2
    Do you know anything else about correlation matrices, other than positive semidefinite? Anything special about their form, how they are calculated?2011-08-26
  • 1
    Bottom line: $-1/(n-1) \le q \le 1$.2011-08-29

3 Answers 3