| Title:
|
Inverse eigenvalue problem of cell matrices (English) |
| Author:
|
Khim, Sreyaun |
| Author:
|
Rodtes, Kijti |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
1015-1027 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the problem of reconstructing an $n \times n$ cell matrix $D(\vec {x})$ constructed from a vector $\vec {x} = (x_{1}, x_{2},\dots , x_{n})$ of positive real numbers, from a given set of spectral data. In addition, we show that the spectra of cell matrices $D(\vec {x})$ and $D(\pi (\vec {x}))$ are the same for every permutation $\pi \in S_{n}$. (English) |
| Keyword:
|
cell matrix |
| Keyword:
|
inverse eigenvalue problem |
| Keyword:
|
Euclidean distance matrix |
| MSC:
|
15B05 |
| MSC:
|
15B10 |
| MSC:
|
15B48 |
| MSC:
|
35P20 |
| MSC:
|
35P30 |
| idZBL:
|
07144871 |
| idMR:
|
MR4039616 |
| DOI:
|
10.21136/CMJ.2019.0579-17 |
| . |
| Date available:
|
2019-11-28T08:49:21Z |
| Last updated:
|
2022-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147910 |
| . |
| Reference:
|
[1] Chu, M. T.: Inverse eigenvalue problems.SIAM Rev. 40 (1998), 1-39. Zbl 0915.15008, MR 1612561, 10.1137/S0036144596303984 |
| Reference:
|
[2] Chu, M. T., Golub, G. H.: Structured inverse eigenvalue problems.Acta Numerica 11 (2002), 1-71. Zbl 1105.65326, MR 2008966, 10.1017/S0962492902000016 |
| Reference:
|
[3] Gyamfi, K. B.: Solution of Inverse Eigenvalue Problem of Certain Singular Hermitian Matrices.Doctoral dissertation, Kwame Nkrumah University of Science and Technology (2012). |
| Reference:
|
[4] Jaklič, G., Modic, J.: On properties of cell matrices.Appl. Math. Comput. 216 (2010), 2016-2023. Zbl 1203.15022, MR 2647070, 10.1016/j.amc.2010.03.032 |
| Reference:
|
[5] Kurata, H., Tarazaga, P.: The cell matrix closest to a given Euclidean distance matrix.Linear Algebra Appl. 485 (2015), 194-207. Zbl 1323.15020, MR 3394144, 10.1016/j.laa.2015.07.030 |
| Reference:
|
[6] Nazari, A. M., Mahdinasab, F.: Inverse eigenvalue problem of distance matrix via orthogonal matrix.Linear Algebra Appl. 450 (2014), 202-216. Zbl 1302.15016, MR 3192478, 10.1016/j.laa.2014.02.017 |
| Reference:
|
[7] Radwan, N.: An inverse eigenvalue problem for symmetric and normal matrices.Linear Algebra Appl. 248 (1996), 101-109. Zbl 0865.15008, MR 1416452, 10.1016/0024-3795(95)00162-X |
| Reference:
|
[8] Schoenberg, I. J.: Metric spaces and positive definite functions.Trans. Am. Math. Soc. 44 (1938), 522-536. Zbl 0019.41502, MR 1501980, 10.1090/S0002-9947-1938-1501980-0 |
| Reference:
|
[9] Tarazaga, P., Kurata, H.: On cell matrices: a class of Euclidean distance matrices.Appl. Math. Comput. 238 (2014), 468-474. Zbl 1334.15090, MR 3209649, 10.1016/j.amc.2014.04.026 |
| Reference:
|
[10] Wang, Z., Zhong, B.: An inverse eigenvalue problem for Jacobi matrices.Math. Probl. Eng. 2011 (2011), Article ID 571781, 11 pages. Zbl 1235.15011, MR 2799869, 10.1155/2011/571781 |
| . |
