I have a large matrix with more columns than rows. I have attempted to row reduce the matrix using Mathematica's RowReduce command. I have been able to do this successfully, but it has taken quite a long time, I think because I'm doing it algebraically rather than numerically (I need to do it this way).

In actual fact I only need the first few rows of the row-reduced matrix (where the algebraic form of the terms is simpler). Is there any way of carrying out a partial row reduction so that I can get the first few rows of the row-reduced matrix without using up all the additional time to do the full process?

Thanks in advance for any help.

  • $\begingroup$ it is not clear what you asking. What is "partial row reduction mean?" it always helps to give an example of an input matrix, and what you want the output to be, instead of just using words. Do you mean you want to obtain the Echelon form (Gaussian elimination phase only) instead of the the full reduced Echelon form? $\endgroup$
    – Nasser
    Aug 23 '21 at 13:54
  • $\begingroup$ As the first row changes with every Gaussian reduction step, you need to do the whole RowReduction to get the first line. $\endgroup$ Aug 23 '21 at 14:11
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    $\begingroup$ Is mathematica.stackexchange.com/q/3069/44520, which shows how to do individual elementary row operations, relevant for you? $\endgroup$ Aug 24 '21 at 6:59
  • $\begingroup$ From these comments, I can see that I haven't really thought this through. It looks like I need to carry out the full row reduction to get even the first few lines correct. Thanks for clarifying. $\endgroup$
    – Chris
    Aug 24 '21 at 11:03