Random matrices and communication systems: WEEK 6 1 Wishart random matrices: joint eigenvalue distribution
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چکیده
Again, this can be viewed as a change of variables; on the left-hand side, there are n diagonal free parameters wjj and n(n−1) 2 off-diagonal free parameters wjk, j < k in the matrix W (the remaining offdiagonal parameters are fixed, as W is symmetric); on the right-hand side, there are n free parameters in the matrix Λ and (n − 1) + (n − 2) + . . . + 1 + 0 = n(n−1) 2 free parameters in the matrix V . So the number of free parameters on both sides coincide. The joint distribution of Λ and V is then given by
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