The Entries of Haar-invariant Matrices from the Classical Compact Groups
نویسنده
چکیده
Let Γn = (γij)n×n be a random matrix with the Haar probability measure on the orthogonal group O(n), the unitary group U(n) or the symplectic group Sp(n). Given 1 ≤ m < n, a probability inequality for a distance between (γij)n×m and some mn independent F -valued normal random variables is obtained, where F = R, C or H (the set of real quaternions). The result is universal for the three cases. In particular, the inequality for Sp(n) is new.
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