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How to track row swap in Gaussian elimination?

Posted 12 years ago
2 Replies

Row swaps are performed for purposes of finding pivots. The strategy used will depend on the nature of the matrix (exact or machine doubles or...).

As for finding the "original position", see remarks in same thread on MSE.

As for why neither post references the other, I've no idea.

POSTED BY: Daniel Lichtblau

Row Reduce doesn't swap rows. From the documentation:

RowReduce performs a version of Gaussian elimination, adding multiples of rows together so as to produce zero elements when possible. The final matrix is in reduced row echelon form.

Do you need to keep track of which rows were added together? There are different ways that the reduction can be done as demonstrated by the "Method" option for the function.

It's possible you might be looking for a specific matrix decomposition instead:

http://en.wikipedia.org/wiki/Orthogonal_matrix#Decompositions

POSTED BY: Sean Clarke
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