I have a general question. I have a large square matrix ($n> 1000$) and it is needed to compute the rank of this matrix. I am reading that the computation of the rank for large matrices, can make numerical problems and the result is not reliable. My question is: Is this correct? And if yes, can you tell me shortly why it is so? And can anyone introduce me some literature which this issue is adressed there?
Thanks in advance, Reza