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Keywords:
generating function; Bézoutian; Hankel matrix
generating function; Bézoutian; Hankel matrix
Summary:
Using the idea of the generating function of a matrix in an extended sense we establish a Bezoutian type formula for a matrix $M$ satisfying an intertwining relation of the form $M A^T = A M$. In the particular case of classical generating functions this formula gives a simple proof of Lander's theorem on the inverse of a Hankel matrix.
References:
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[2] G. Heinig K. Rost: Algebraic Methods for Toeplitz-like matrices and operators. Akademie-Verlag Berlin (1984). MR 0782105
[3] F. I. Lander: The Bezoutian and the inversion of Hankel and Toeplitz matrices. Matem. Issled. Kishinev 9 (1974), 69-87. (In Russian.) MR 0437559
[4] V. Pták: The infinite companion matrix. Lin. Algebra Appl. 166 (1992), 65-95. DOI 10.1016/0024-3795(92)90270-K | MR 1152488
[5] O. Taussky H. Zassenhaus: On the similarity transformation between a matrix and its transpose. Pacific J. Math. 9 (1959), 893-896. DOI 10.2140/pjm.1959.9.893 | MR 0108500
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