| Title:
|
Sylvesterovy–Hadamardovy, Kravčukovy a Sylvesterovy–Kacovy matice (Czech) |
| Title:
|
Sylvester–Hadamard matrices, Krawtchouk matrices and Sylvester–Kac matrices (English) |
| Author:
|
Štěpánová, Martina |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
81-101 |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Je zcela běžné, že speciální třídy matic jsou pojmenovány podle matematika, který je buď poprvé představil nebo podstatně přispěl k jejich studiu. Článek je věnován třem třídám matic nesoucích ve svých názvech jména čtyř matematiků: Sylvesterovým–Hadamardovým maticím, Kravčukovým maticím a Sylvesterovým–Kacovým maticím. Přestože na první pohled nemají uvedené třídy příliš společného, jsou v textu ukázány jejich vzájemné souvislosti. (Czech) |
| MSC:
|
01A55 |
| MSC:
|
01A60 |
| MSC:
|
15-03 |
| MSC:
|
15B10 |
| MSC:
|
15B34 |
| MSC:
|
15B36 |
| MSC:
|
15B99 |
| . |
| Date available:
|
2017-07-10T08:45:41Z |
| Last updated:
|
2018-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146811 |
| . |
| Reference:
|
[1] Bose, N.: Digital filters: theory and applications.. North-Holland, Amsterdam, 1985. Zbl 0588.94011 |
| Reference:
|
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| Reference:
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[3] Feinsilver, P., Kocik, J.: Krawtchouk polynomials and Krawtchouk matrices.. In Baeza-Yates, R., Glaz, J., Gzyl, H., Hüsler, J., Palacios, J. L. (eds.): Recent Advances in Applied Probability, Springer-Verlag, Boston, 2005, 115–141. Zbl 1075.33003, MR 2102950 |
| Reference:
|
[4] Hadamard, J.: Résolution d’une question relative aux déterminants.. Bull. des Sci. Math. 17 (1893), 240–246. |
| Reference:
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[5] Horadam, K. J.: Hadamard matrices and their applications.. Princeton University Press, Princeton, 2006. MR 2265694 |
| Reference:
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| Reference:
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[7] Kac, M.: Probability and related topics in physical sciences.. Interscience Publishers, New York, 1959. Zbl 0087.33003, MR 0106225 |
| Reference:
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[8] Kharaghani, H., Tayfeh-Rezaie, B.: A Hadamard matrix of order 428.. J. Comb. Des. 13 (2005), 435–440. Zbl 1076.05017, MR 2221851, 10.1002/jcd.20043 |
| Reference:
|
[9] Kocik, J.: Krawtchouk matrices, Feynman path integral and the split quaternions.. In Budzban, G., Hughes, H. R., Schurz, H., (eds.): Probability on algebraic and geometric structures, AMS, 2016, 131–164. MR 3536697 |
| Reference:
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[10] Krawtchouk, M.: Sur une généralisation des polynomes d’Hermite.. C. R. Acad. Sci. 189 (1929), 620–622. |
| Reference:
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[11] Krawtchouk, M.: Sur la distribution des racines des polynomes orthogonaux.. C. R. Acad. Sci. 196 (1933), 739–741. Zbl 0006.19601 |
| Reference:
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[12] Lampio, P. H. J.: Classificaton of difference matrices and complex Hadamard matrices.. Aalto University publication series Doctoral dissertations 177/2015, Helsinki, 2015. |
| Reference:
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[13] Mitrouli, M.: Sylvester Hadamard matrices revisited.. Spec. Matrices 2 (2014), 120–124. Zbl 1310.15056, MR 3155411 |
| Reference:
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[14] O’Connor, J. J., Robertson, E. F.: Mark Kac.. http://www-history.mcs.st-andrews.ac.uk/Biographies/kac.html. |
| Reference:
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[15] Paley, R. E. A. C.: On orthogonal matrices.. J. Math. Phys. 12 (1933), 311–320. Zbl 0007.10004, 10.1002/sapm1933121311 |
| Reference:
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[16] Seberry, J., Yamada, M.: Hadamard matrices, sequences, and block designs.. In Stinson, D. J., Dinitz, J. (eds.): Contemporary Design Theory–A Collection of Surveys, John Wiley, 1992, 431–560. Zbl 0776.05028, MR 1178508 |
| Reference:
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[17] Schrödinger, R.: Quantisierung als Eigenwertproblem (Dritte Mitteilung).. Ann. Phys. 80 (1926), 437–490. 10.1002/andp.19263851302 |
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| Reference:
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[19] Sylvester, J. J.: Thoughts on inverse orthogonal matrices, simultaneous sign-successions, and tessellated pavements in two or more colours, with applications to Newton’s rule, ornamental tile-work, and the theory of numbers.. Phil. Mag. 34 (1867), 461–475. |
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[20] Štěpánová, M.: Olga Taussky-Todd: z Olomouce do Pasadeny.. Pokroky Mat. Fyz. Astronom. 61 (2016), 197–213. |
| Reference:
|
[21] Taussky-Todd, O., Todd, J.: Another look at a matrix of Mark Kac.. Linear Algebra Appl. 150 (1991), 341–360. MR 1102076 |
| . |
