Article
| Title: | A geometric construction for spectrally arbitrary sign pattern matrices and the $2n$-conjecture (English) |
| Author: | Jadhav, Dipak |
| Author: | Deore, Rajendra |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 565-580 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We develop a geometric method for studying the spectral arbitrariness of a given sign pattern matrix. The method also provides a computational way of computing matrix realizations for a given characteristic polynomial. We also provide a partial answer to $2n$-conjecture. We determine that the $2n$-conjecture holds for the class of spectrally arbitrary patterns that have a column or row with at least $n-1$ nonzero entries. (English) |
| Keyword: | spectrally arbitrary sign pattern |
| Keyword: | $2n$-conjecture |
| MSC: | 15B35 |
| idZBL: | Zbl 07729524 |
| idMR: | MR4586911 |
| DOI: | 10.21136/CMJ.2023.0132-22 |
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| Date available: | 2023-05-04T17:49:59Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151674 |
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| Reference: | [1] Bergsma, H., Meulen, K. N. Vander, Tuyl, A. Van: Potentially nilpotent patterns and the Nilpotent-Jacobian method.Linear Algebra Appl. 436 (2012), 4433-4445. Zbl 1244.15019, MR 2917420, 10.1016/j.laa.2011.05.017 |
| Reference: | [2] Britz, T., McDonald, J. J., Olesky, D. D., Driessche, P. van den: Minimal spectrally arbitrary sign patterns.SIAM J. Matrix Anal. Appl. 26 (2004), 257-271. Zbl 1082.15016, MR 2112860, 10.1137/S0895479803432514 |
| Reference: | [3] Brualdi, R. A., Carmona, Á., Driessche, P. van den, Kirkland, S., Stevanović, D.: Combinatorial Matrix Theory.Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser, Cham (2018). Zbl 1396.05002, MR 3791450, 10.1007/978-3-319-70953-6 |
| Reference: | [4] Catral, M., Olesky, D. D., Driessche, P. van den: Allow problems concerning spectral properties of sign pattern matrices : A survey.Linear Algebra Appl. 430 (2009), 3080-3094. Zbl 1165.15009, MR 2517861, 10.1016/j.laa.2009.01.031 |
| Reference: | [5] Cavers, M. S., Fallat, S. M.: Allow problems concerning spectral properties of patterns.Electron. J. Linear Algebra 23 (2012), 731-754. Zbl 1251.15034, MR 2966802, 10.13001/1081-3810.1553 |
| Reference: | [6] Deaett, L., Garnett, C.: Algebraic conditions and the sparsity of spectrally arbitrary patterns.Spec. Matrices 9 (2021), 257-274. Zbl 1478.15045, MR 4249690, 10.1515/spma-2020-0136 |
| Reference: | [7] Garnett, C., Shader, B. L.: A proof of the $T_n$ conjecture: Centralizers, Jacobians and spectrally arbitrary sign patterns.Linear Algebra Appl. 436 (2012), 4451-4458. Zbl 1244.15020, MR 2917422, 10.1016/j.laa.2011.06.051 |
| Reference: | [8] Hall, F. J., Li, Z.: Sign pattern matrices.Handbook of Linear Algebra Chapman and Hall/CRC, New York (2018), Chapter 33-1. 10.1201/9781420010572 |
| Reference: | [9] Quirk, J., Ruppert, R.: Qualitative economics and the stability of equilibrium.Rev. Econ. Stud. 32 (1965), 311-326. 10.2307/2295838 |
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