Additive decomposition of matrices under rank conditions and zero pattern constraints

Harm Bart; Torsten Ehrhardt

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 3, page 825-854
  • ISSN: 0011-4642

Abstract

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This paper deals with additive decompositions A = A 1 + ⋯ + A p of a given matrix A , where the ranks of the summands A 1 , ... , A p are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs.

How to cite

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Bart, Harm, and Ehrhardt, Torsten. "Additive decomposition of matrices under rank conditions and zero pattern constraints." Czechoslovak Mathematical Journal 72.3 (2022): 825-854. <http://eudml.org/doc/298460>.

@article{Bart2022,
abstract = {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.},
author = {Bart, Harm, Ehrhardt, Torsten},
journal = {Czechoslovak Mathematical Journal},
keywords = {additive decomposition; rank constraint; zero pattern constraint; directed bipartite graph; $ß\{L\}$-free directed bipartite graph; permutation $ß\{L\}$-free directed bipartite graph; Bell number; Stirling partition number},
language = {eng},
number = {3},
pages = {825-854},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Additive decomposition of matrices under rank conditions and zero pattern constraints},
url = {http://eudml.org/doc/298460},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Bart, Harm
AU - Ehrhardt, Torsten
TI - Additive decomposition of matrices under rank conditions and zero pattern constraints
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 3
SP - 825
EP - 854
AB - 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.
LA - eng
KW - additive decomposition; rank constraint; zero pattern constraint; directed bipartite graph; $ß{L}$-free directed bipartite graph; permutation $ß{L}$-free directed bipartite graph; Bell number; Stirling partition number
UR - http://eudml.org/doc/298460
ER -

References

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  1. Bart, H., Ehrhardt, T., Silbermann, B., 10.1007/s10587-016-0305-7, Czech. Math. J. 66 (2016), 987-1005. (2016) Zbl1413.15010MR3556880DOI10.1007/s10587-016-0305-7
  2. Bart, H., Ehrhardt, T., Silbermann, B., 10.1007/978-3-319-49182-0_8, Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics Operator Theory: Advances and Applications 259. Birkhäuser, Basel (2017), 79-124. (2017) Zbl1365.15014MR3644514DOI10.1007/978-3-319-49182-0_8
  3. Bart, H., Ehrhardt, T., Silbermann, B., 10.1007/978-3-030-04269-1_3, Operator Theory, Analysis and the State Space Approach Operator Theory: Advances and Applications 271. Birkhäuser, Cham (2018), 75-117. (2018) Zbl1427.15016MR3889652DOI10.1007/978-3-030-04269-1_3
  4. Bart, H., Ehrhardt, T., Silbermann, B., 10.1016/j.laa.2021.03.010, Linear Algebra Appl. 621 (2021), 135-180. (2021) Zbl1464.15002MR4231570DOI10.1016/j.laa.2021.03.010
  5. Bart, H., Wagelmans, A. P. M., 10.1016/S0024-3795(99)00219-0, Linear Algebra Appl. 305 (2000), 107-129. (2000) Zbl0951.15013MR1733797DOI10.1016/S0024-3795(99)00219-0
  6. Birkhoff, G., 10.1090/coll/025, American Mathematical Society Colloquium Publications 25. AMS, Providence (1967). (1967) Zbl0153.02501MR0227053DOI10.1090/coll/025
  7. Charalambides, C. A., 10.1201/9781315273112, CRC Press Series on Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton (2002). (2002) Zbl1001.05001MR1937238DOI10.1201/9781315273112
  8. Habib, M., Jegou, R., 10.1016/0166-218X(85)90030-7, Discrete Appl. Math. 12 (1985), 279-291. (1985) Zbl0635.06002MR0813975DOI10.1016/0166-218X(85)90030-7
  9. Riordan, J., Combinatorial Identities, John Wiley & Sons, New York (1968). (1968) Zbl0194.00502MR0231725
  10. Stanley, R. P., 10.1017/CBO9780511805967, Cambridge Studies in Advanced Mathematics 49. Cambridge University Press, Cambridge (1997). (1997) Zbl0889.05001MR1442260DOI10.1017/CBO9780511805967

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