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,
 
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One can always separate the zeroes first and deal with the rest.
 

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