| Title:
|
Additive decomposition of matrices under rank conditions and zero pattern constraints (English) |
| Author:
|
Bart, Harm |
| Author:
|
Ehrhardt, Torsten |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
825-854 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with additive decompositions $A=A_1+\cdots +A_p$ of a given matrix $A$, where the ranks of the summands $A_1,\ldots , A_p$ are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs. (English) |
| Keyword:
|
additive decomposition |
| Keyword:
|
rank constraint |
| Keyword:
|
zero pattern constraint |
| Keyword:
|
directed bipartite graph |
| Keyword:
|
$ß{L}$-free directed bipartite graph |
| Keyword:
|
permutation $ß{L}$-free directed bipartite graph |
| Keyword:
|
Bell number |
| Keyword:
|
Stirling partition number |
| MSC:
|
05C20 |
| MSC:
|
05C50 |
| MSC:
|
15A03 |
| MSC:
|
15A21 |
| idZBL:
|
Zbl 07584105 |
| idMR:
|
MR4467945 |
| DOI:
|
10.21136/CMJ.2022.0185-21 |
| . |
| Date available:
|
2022-08-22T08:24:45Z |
| Last updated:
|
2024-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150620 |
| . |
| Reference:
|
[1] Bart, H., Ehrhardt, T., Silbermann, B.: Rank decomposition in zero pattern matrix algebras.Czech. Math. J. 66 (2016), 987-1005. Zbl 1413.15010, MR 3556880, 10.1007/s10587-016-0305-7 |
| Reference:
|
[2] Bart, H., Ehrhardt, T., Silbermann, B.: Echelon type canonical forms in upper triangular matrix algebras.Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics Operator Theory: Advances and Applications 259. Birkhäuser, Basel (2017), 79-124. Zbl 1365.15014, MR 3644514, 10.1007/978-3-319-49182-0_8 |
| Reference:
|
[3] Bart, H., Ehrhardt, T., Silbermann, B.: $ß{L}$-free directed bipartite graphs and echelon-type canonical forms.Operator Theory, Analysis and the State Space Approach Operator Theory: Advances and Applications 271. Birkhäuser, Cham (2018), 75-117. Zbl 1427.15016, MR 3889652, 10.1007/978-3-030-04269-1_3 |
| Reference:
|
[4] Bart, H., Ehrhardt, T., Silbermann, B.: Rank decomposition under zero pattern constraints and $ß{L}$-free directed graphs.Linear Algebra Appl. 621 (2021), 135-180. Zbl 1464.15002, MR 4231570, 10.1016/j.laa.2021.03.010 |
| Reference:
|
[5] Bart, H., Wagelmans, A. P. M.: An integer programming problem and rank decomposition of block upper triangular matrices.Linear Algebra Appl. 305 (2000), 107-129. Zbl 0951.15013, MR 1733797, 10.1016/S0024-3795(99)00219-0 |
| Reference:
|
[6] Birkhoff, G.: Lattice Theory.American Mathematical Society Colloquium Publications 25. AMS, Providence (1967). Zbl 0153.02501, MR 0227053, 10.1090/coll/025 |
| Reference:
|
[7] Charalambides, C. A.: Enumerative Combinatorics.CRC Press Series on Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton (2002). Zbl 1001.05001, MR 1937238, 10.1201/9781315273112 |
| Reference:
|
[8] Habib, M., Jegou, R.: $N$-free posets as generalizations of series-parallel posets.Discrete Appl. Math. 12 (1985), 279-291. Zbl 0635.06002, MR 0813975, 10.1016/0166-218X(85)90030-7 |
| Reference:
|
[9] Riordan, J.: Combinatorial Identities.John Wiley & Sons, New York (1968). Zbl 0194.00502, MR 0231725 |
| Reference:
|
[10] Stanley, R. P.: Enumerative Combinatorics. Vol. 1.Cambridge Studies in Advanced Mathematics 49. Cambridge University Press, Cambridge (1997). Zbl 0889.05001, MR 1442260, 10.1017/CBO9780511805967 |
| . |
