On the rank of a tropical matrix

Maja Ilc (2012) On the rank of a tropical matrix. EngD thesis.

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Abstract

Rank of a real matrix can be defined in many equivalent way. It is interesting that the rank of a matrix over the tropical semiring can vary according to these definitions, which means that the ways in which we can determine rank are no longer equivalent. In the thesis we focus on three rank definitions; rank of a matrix determined by the maximum regular minor, row rank and column rank. We demonstrate with example that with the extension of tropical semiring we can achieve similar results to those over reals.

Item Type:

Thesis (EngD thesis)

Keywords:

Tropical algebra, tropical semiring, determinant of a matrix, dependence of vectors, singular matrix, tropical rank

Number of Pages:

Language of Content:

Slovenian

Mentor / Comentors:

Name and Surname	ID	Function
doc. dr. Polona Oblak	6760	Mentor

Link to COBISS:

http://www.cobiss.si/scripts/cobiss?command=search&base=50070&select=(ID=00009487700)

Institution:

University of Ljubljana

Department:

Faculty of Computer and Information Science

Item ID:

1861

Date Deposited:

24 Sep 2012 16:22

Last Modified:

06 Nov 2012 08:35

URI:

http://eprints.fri.uni-lj.si/id/eprint/1861

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