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On the Determinant of a Uniformly Distributed Complex Matrix |
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| Institution: | MIT, Dept Math, Cambridge, MA 02139. |
| Abstract: | We derive the joint density for the singular values of a random complex matrix A uniformly distributed on ||A||F = 1 This joint density allows us to obtain the conditional expectation of det(AHA) = |det A|2 given the smallest singular value. This result has been used by Shub and Smale in their analysis of the complexity of Bezout′s theorem. |
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