| Title:
|
Generating functions and Bézoutians (English) |
| Author:
|
Pták, Vlastimil |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
121 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
183-188 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
generating function |
| Keyword:
|
Bézoutian |
| Keyword:
|
Hankel matrix |
| MSC:
|
15A09 |
| MSC:
|
15A57 |
| idZBL:
|
Zbl 0863.15002 |
| idMR:
|
MR1400611 |
| DOI:
|
10.21136/MB.1996.126101 |
| . |
| Date available:
|
2009-09-24T21:18:15Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126101 |
| . |
| Reference:
|
[1] A. Fiedler V. Pták: Intertwining and testing matrices corresponding to a polynomial.Lin. Algebra Appl. 86 (1987), 53-74. MR 0870932, 10.1016/0024-3795(87)90287-4 |
| Reference:
|
[2] G. Heinig K. Rost: Algebraic Methods for Toeplitz-like matrices and operators.Akademie-Verlag Berlin (1984). MR 0782105 |
| Reference:
|
[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 |
| Reference:
|
[4] V. Pták: The infinite companion matrix.Lin. Algebra Appl. 166 (1992), 65-95. MR 1152488, 10.1016/0024-3795(92)90270-K |
| Reference:
|
[5] O. Taussky H. Zassenhaus: On the similarity transformation between a matrix and its transpose.Pacific J. Math. 9 (1959), 893-896. MR 0108500, 10.2140/pjm.1959.9.893 |
| . |
