<p>Essentially yes, unlike Cholesky decomposition the LUP decomposition only uses generic field operations, so it can be applied to finite fields as well (and moreover, the result is useful). For pseudo code and further discussion about linear algebra over finite fields, see for example <a href="https://arxiv.org/pdf/1204.3735.pdf" rel="nofollow noreferrer">Computational linear algebra over finite fields</a>.</p>

<p>Even more specifically relevant is <a href="https://pdfs.semanticscholar.org/0e71/9c72fe2f2e9cd5c9c1ffe27dc546fd0a15c0.pdf" rel="nofollow noreferrer">Fast matrix decomposition in ₂</a>.</p>

<p>FFPACK has a ready to use implementation of several BLAS-like routines but over finite fields, including decomposition.</p>
LUP - decomposition of a boolean matrix: any pointers
<p>I'm currently working on the following problem: I pretty much have to perform (find) LUP decomposition of the boolean matrix. My question is: in LUP decomposition algorithm (LUP), if I somehow substitute operations for division and subtraction to those, defined for boolean scope - will it produce the desired result? Also, looking for any pointers - the problem seems unsolvable to me at the moment.
Thanks for any response in advance.</p>