Abstract
Let Γ n =(γ ij )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 (γ ij )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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.