Operator-valued Free Fisher Information of Random Matrices
نویسنده
چکیده
We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for Φ M2(B) (A,A,M2(B), η), where A ∈ M2(B) is a 2 × 2 operator matrix on B, and η is linear operators on M2(B). Then we consider a special setting: A is an operator-valued semicircular matrix with conditional expectation covariance, and find that Φ B (c, c : B, id) = 2Index(E), where E is a conditional expectation of B onto D and c is a circular variable with covariance E.
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