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Block Jacobi Matrices and Zeros of Multivariate Orthogonal Polynomials
Transactions of the American Mathematical Society
Vol. 342, No. 2 (Apr., 1994), pp. 855-866
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2154656
Page Count: 12
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A commuting family of symmetric matrices are called the block Jacobi matrices, if they are block tridiagonal. They are related to multivariate orthogonal polynomials. We study their eigenvalues and joint eigenvectors. The joint eigenvalues of the truncated block Jacobi matrices correspond to the common zeros of the multivariate orthogonal polynomials.
Transactions of the American Mathematical Society © 1994 American Mathematical Society