A companion matrix analogue for orthogonal polynomials

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Given a set of orthogonal polynomials {Pi(x)}, it is shown that associated with a polynomial a(x)=∑aipi(x) there is a matrix A which possesses several of the properties of the usual companion form matrix C. An alternative and possibly preferable form A' is also suggested. A similarity transformation between A [orA'] and C is given. If b(x) is another polynomial then the matrix b(A) [or b(A')] has properties like those of b(C), relating to the greatest common divisor of a(x) and b(x). © 1975.




Barnett, S. (1975). A companion matrix analogue for orthogonal polynomials. Linear Algebra and Its Applications, 12(3), 197–202. https://doi.org/10.1016/0024-3795(75)90041-5

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