Matrix prerequisities for Gauss elimination

Ronankeating
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hi all,

Is there any matrix pre-requisities for Gauss elimination. Working on linear equations, I think I 've composed the global(stiffness) matrix of the LHS of linear equation.And found on the net the working code which uses Gauss elimination method, in the code beginning it checks non-zero values of diagonal term, if it founds algorithm exits.
Since I'm not fully conversant everything in depth, I assume that none of the diagonal products shouldn't be zero and therefore my global stiffness matrix is ill conditioned?

Any comment will be appreciated,
 
One can always separate the zeroes first and deal with the rest.
 

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