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Journal of Computational Biology
Characterization of Complex Biological Systems by Matrix Invariants
To cite this article:
Gašper Jaklič, Tomaž Pisanski, Milan Randić.
Journal of Computational Biology.
November 2006,
13(9): 1558-1564.
doi:10.1089/cmb.2006.13.1558.
Published in Volume: 13 Issue 9: December 5, 2006
Dr. Gašper Jaklič Department of Theoretical Computer Science, Institute of Mathematics, Physics and Mechanics (IMFM), University of Ljubljana, Slovenia. Tomaž Pisanski Department of Theoretical Computer Science, Institute of Mathematics, Physics and Mechanics (IMFM), University of Ljubljana, Slovenia. UP PINT, University of Primorska, Slovenia. Milan Randić Emeritus, Department of Mathematics and Computer Science, Drake University, and National Institute of Chemistry, Slovenia. 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/˜jaklicg/ldmatrix.html.
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