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I have to solve system of linear algebraic equations AX=B, where A is two-dimensional matrix and all elements of main diagonal are equal to zero.

How to solve this problem? Iterational methods are not applied in this case.

One way is LU Decomposition method with reordering rows of A to get entries in main diagonal are not zero using permutation matrix. How to quickly reorder rows of matrix or find permutation matrix?

Note that matrix is very big and I have to write programm to solve SLAE in C# language, so I do not need any matlab or mathematica functions. Thanks!

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    Not sure if this belongs here or over at cs.stackexchange.com...2012-12-25
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    What do you mean with _two-dimensional_ matrix? Normally one would interpret that as a $2\times2$ matrix, but this seems to contradict "matrix is very big". Do you just means that the matrix can be written in a two-dimensional layout? This is true for _all_ matrices, so if you mean that just drop the phrase.2012-12-25
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    @MarcvanLeeuwen It may be a misuse of terminology, as I have seen the term 'matrix' applied to higher dimensional arrays of data in the computational sciences.2012-12-25
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    I mean usual two-dimensional matrix nxn, with n > 500000. like this http://3.bp.blogspot.com/_264sc_gncA4/SiEOApq5oaI/AAAAAAAAAVE/DG_mb6OI7r0/s400/Session8-two-dim+array.png2012-12-27

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