Characterization of complex biological systems by matrix invariants.
One direction in exploring similarities among biological sequences (such as DNA, RNA, and proteins), is to associate with such systems ordered sets of sequence invariants. These invariants represent selected properties of mathematical objects, such as matrices, that one can associate with biological sequences. In this article, we are exploring properties of recently introduced Line Distance matrices, and in particular we consider properties of their eigenvalues. We prove that Line Distance matrices of size n have one positive and n - 1 negative eigenvalues. Visual representation of Cauchy's interlacing property for Line Distance matrices is considered. Matlab programs for line distance matrices and examples are available on the following website: www.fmf.uni-lj.si/ approximately jaklicg/ldmatrix.html.
Jaklic
Gasper
G
Department of Theoretical Computer Science, Institute of Mathematics, Physics and Mechanics (IMFM), University of Ljubljana, Slovenia. gasper.jaklic@fmf.uni-lj.si
Pisanski
Tomaz
T
Randić
Milan
M
D001699:Biometry; D004247:DNA / Q000235:genetics; D008954:Models, Biological; D015233:Models, Statistical; D016415:Sequence Alignment / Q000706:statistics & numerical data; D012984:Software
D004247:DNA