Eigenvectors under scaling/ matrix approximation

* corresponds to matrix product

I'm working on a method of visualising graphs, and that method uses eigenvector computations. For a certain square matrix K (the entries of which are result of C_transpose*C, therefore K is symmetric) I have to compute the eigenvectors.

Since C is mXn, where m>>n, I go with a portion of C (NOT the dot product of the COMPLETE first row of C_transpose with the complete first column of C, but the portion (1/5 perhaps), meaning the dot product of the PORTION of the first row of C_transpose with the portion of the first column of C). In order to get good approximation of the original COMPLETE C_transpose*C, I'm not sure whether I need to multiply each entry of K with 5 (see 1/5 above).

How would the eigenvectors behave if I do not perform the multiplication with 5?

In addition, any other suggestion how to approximate C_transpose*C, where C is mXn matrix, with m>>n are very welcome.

I hope I explained the problem properly.

Thanks