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Max-Planck-Institut für Informatik: Computer Algebra

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I'm learning about the Bareiss algorithm to compute determinants over integral domains from Chee Yap, Fundamental Problems of Algorithmic Algebra see also this question. The naive version of the algorithm suffers from zero divisions, i. As mentioned briefly in the text - and also more extensively in this paper p. There is some hint later on in the Yap text about this meaning that the matrix has dependent rows so the determinant would be 0.

But I don't have a proof for this.

Additionally, it would be useful if somebody knew a concrete example of a matrix that exhibits this behaviour. The only one I can think of is the zero matrix which, trivially, does have determinant 0.

Steels: Metallurgy and Applications, Third Edition

First, let's assume wlog that no row exchanges have happend up to the point where we cannot find a suitable row for the row exchange because one can show that this would be equivalent to computing the determinant of the same matrix with the rows exchanged initially; that matrix has determinant 0 iff the original one has determinant 0. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Pivoting in the Bareiss algorithm Ask Question.

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