TY  - CHAP
A1  - Al Muhtaseb, Khawla
A1  - Adm, Mohammad
A1  - Ghani, Ayed Abedel
A1  - Garloff, Jürgen
T1  - Recent applications of the Cauchon algorithm to intervals of totally nonnegative matrices
T2  - Sixth Palestinian Conference on Modern Trends in Mathematics and Physics (PCMTMP-VI), 5. - 8. August 2018, Palestine Technical University Kadoorei, Palästina
KW  - Totally nonnegative matrix
KW  - Matrix interval
KW  - Checkerboard partial ordering
KW  - Cauchon algorithm
Y1  - 2018
ER  - 
TY  - CHAP
A1  - Ghani, Ayed Abedel
A1  - Adm, Mohammad
A1  - Al Muhtaseb, Khawla
A1  - Fallat, Shaun M.
A1  - Garloff, Jürgen
T1  - A novel method for determining the rank of a matrix
T2  - Sixth Palestinian Conference on Modern Trends in Mathematics and Physics (PCMTMP-VI), 5. - 8. August 2018, Palestine Technical University Kadoorei, Palästina
KW  - Rank
KW  - Linear independence
KW  - Cauchon algorithm
Y1  - 2018
ER  - 
TY  - JOUR
A1  - Adm, Mohammad
A1  - Al Muhtaseb, Khawla
A1  - Ghani, Ayed Abedel
A1  - Fallat, Shaun M.
A1  - Garloff, Jürgen
T1  - Further applications of the Cauchon algorithm to rank determination and bidiagonal factorization
JF  - Linear Algebra and its Applications
N2  - For a class of matrices connected with Cauchon diagrams, Cauchon matrices, and the Cauchon algorithm, a method for determining the rank, and for checking a set of consecutive row (or column) vectors for linear independence is presented. Cauchon diagrams are also linked to the elementary bidiagonal factorization of a matrix and to certain types of rank conditions associated with submatrices called descending rank conditions.
KW  - Rank
KW  - Cauchon matrix
KW  - Cauchon diagram
KW  - Cauchon algorithm
Y1  - 2018
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bsz:kon4-opus4-14604
SN  - 0024-3795
SN  - 1873-1856
VL  - 545
SP  - 240
EP  - 255
ER  - 
TY  - CHAP
A1  - Garloff, Jürgen
A1  - Adm, Mohammad
A1  - Al Muhtaseb, Khawla
A1  - Ghani, Ayed Abedel
T1  - Relaxing the nonsingularity assumption  for intervals of totally nonnegative matrices
T2  - MAT TRIAD 2019 Book of Abtracts, International Conference on Matrix Analysis and its Applications, September 8-13, Liblice, Czech Republic (IUUK-CE-ITI series 2019)
Y1  - 2019
UR  - https://mattriad.math.cas.cz//programme/
SP  - 23
EP  - 23
ER  - 
TY  - JOUR
A1  - Adm, Mohammad
A1  - Al Muhtaseb, Khawla
A1  - Ghani, Ayed Abedel
A1  - Garloff, Jürgen
T1  - Relaxing the nonsingularity assumption for intervals of totally nonnegative matrices
JF  - Electronic Journal of Linear Algebra (ELA)
N2  - Totally nonnegative matrices, i.e., matrices having all their minors nonnegative, and matrix intervals with respect to the checkerboard partial order are considered. It is proven that if the two bound matrices of such a matrix interval are totally nonnegative and satisfy certain conditions, then all matrices from this interval are also totally nonnegative and satisfy the same conditions.
KW  - Matrix interval
KW  - Checkerboard partial order
KW  - Totally nonnegative matrix
KW  - Descending rank conditions
KW  - Cauchon algorithm
Y1  - 2020
U6  - http://dx.doi.org/10.13001/ela.2020.5015
SN  - 1081-3810
VL  - Vol. 36
SP  - 106
EP  - 123
ER  -