Is it possible to scale the eigenvector matrix up by multiplying or adding with a constant? I am using R to generate eigenvector matrix from laplacian matrix that represent a graph dataset. The issue that I have is that the values of eigenvector matrix are very much low, sometimes in the order of $10^{-20}$! My question is: is it possible to scale the eigenvector matrix up by multiplying or adding with a constant? I think by doing this, it will increase the magnitude of vectors but I am worried that it may destroy the direction of the vectors.
Thank you very much

Yes, it is, since the space of all eigenvectors corresponding to an specific eigenvalue is a vector space, so if you multiply them by nonzero constant or even add them you  will still get an eigenvector.
