## The beta-Jacobi matrix model, the CS decomposition, and generalized singular value problems

Alan Edelman and Brian D. Sutton
*Found. Comput. Math.* 8 (2008), no. 2, 259–285.

We provide a solution to the beta-Jacobi matrix model problem
posed by Dumitriu and the first author. The random matrix distribution introduced here,
called a matrix model, is related to the model of Killip and Nenciu, but the development is
quite different. We start by introducing a new matrix decomposition and an algorithm
for computing this decomposition. Then we run the algorithm on a Haar-distributed
random matrix to produce the beta-Jacobi matrix model.
This new random matrix distribution in a sense extends Haar measure on the orthogonal (beta = 1)
and unitary (beta = 2) groups to general beta and reveals some new connections between
random matrix theory and the CS decomposition.

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