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Xiaonan Hu, Charles R. Johnson, Caroline E. Davis, Yimeng Zhang (2016)
Special Matrices
A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.
Georges Dostor (1873)
Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale
Ferrante, Augusto, Wimmer, Harald K. (2010)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Marcellán, F., Yakhlef, H. O. (2002)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Benjamin, Arthur T., Shattuck, Mark A. (2007)
Integers
Han, Guo-Niu, Krattenthaler, Christian (1999)
Séminaire Lotharingien de Combinatoire [electronic only]
Fricke, Gerd H., Hedetniemi, Stephen T., Jacobs, David P., Trevisan, Vilmar (1996)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Fischer, Cyril, Náprstek, Jiří (2017)
Programs and Algorithms of Numerical Mathematics
Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes an implementation...
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