Generating functions and Bézoutians

Vlastimil Pták

Mathematica Bohemica (1996)

  • Volume: 121, Issue: 2, page 183-188
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Pták, Vlastimil. "Generating functions and Bézoutians." Mathematica Bohemica 121.2 (1996): 183-188. <http://eudml.org/doc/247972>.

@article{Pták1996,
abstract = {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.},
author = {Pták, Vlastimil},
journal = {Mathematica Bohemica},
keywords = {generating function; Bézoutian; Hankel matrix; generating function; Bézoutian; Hankel matrix},
language = {eng},
number = {2},
pages = {183-188},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generating functions and Bézoutians},
url = {http://eudml.org/doc/247972},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Pták, Vlastimil
TI - Generating functions and Bézoutians
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 2
SP - 183
EP - 188
AB - 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.
LA - eng
KW - generating function; Bézoutian; Hankel matrix; generating function; Bézoutian; Hankel matrix
UR - http://eudml.org/doc/247972
ER -

References

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  1. A. Fiedler V. Pták, 10.1016/0024-3795(87)90287-4, Lin. Algebra Appl. 86 (1987), 53-74. (1987) MR0870932DOI10.1016/0024-3795(87)90287-4
  2. G. Heinig K. Rost, Algebraic Methods for Toeplitz-like matrices and operators, Akademie-Verlag Berlin (1984). (1984) MR0782105
  3. F. I. Lander, The Bezoutian and the inversion of Hankel and Toeplitz matrices, Matem. Issled. Kishinev 9 (1974), 69-87. (In Russian.) (1974) MR0437559
  4. V. Pták, 10.1016/0024-3795(92)90270-K, Lin. Algebra Appl. 166 (1992), 65-95. (1992) MR1152488DOI10.1016/0024-3795(92)90270-K
  5. O. Taussky H. Zassenhaus, 10.2140/pjm.1959.9.893, Pacific J. Math. 9 (1959), 893-896. (1959) MR0108500DOI10.2140/pjm.1959.9.893

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