Question: Export data produced in a loop

Hello everyone I have a question about the use of ExportMatrix and ExportVector. I am currently working on a sheet, where a matrix is changed within a loop. At the end of each cycle of the loop, the eigenvalues of the matrix are calculated and given out in form of a vector. How can I export these eigenvalue-vectors to a textfile together with the index of the loop? I already tried to use ExportVector at the end of each cycle, but the command overwrites entries of previous cycles, so that only the very last eigenvalue-vector is noted. Thank you very much for any help.
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