Abstract
We derive an explicit formula for the R-transform of inverse Jacobi matrix I + W 1 -1 W 2 , where W 1 , W 2 ~ W p ( I , n i ), i = 1, 2 are independent and I is pxp dimensional identity matrix using property of asymptotic freeness of Wishart and deterministic matrices. Procedure can be extended to other sets of the asymptotically free independent matrices. Calculations are illustrated with some simulations on fixed size matrices. Keywords: Jacobi ensemble; R-transform; S-transform; Negative spectral moments; Spectral moments; Wishart matrix; Marcenko – Pastur law; asymptotical freeness
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