# How to Obtain Similar Eigenvalues

1. Jun 21, 2009

### expi123

Hi!
I have a 100 X 100 matrix and I want to modify it (by adding any number of additional rows) to obtain almost all the eigenvalues quite similar. The main conditions on the matrix are that no entries in the matrix can have values of 0 (all entries are from 1 to 15). I think for a 2 X 2 matrix the two eigenvalues can be made equal if the matrix is diagonal (i.e. all entries apart from the main diagonals are zeroes). This cannot be accepted because of zeroes.
I have found how to test if the eigenvalues are equal on the following websites:
http://www.fon.hum.uva.nl/praat/manual/PCA__Get_equality_of_eigenvalues___.html
http://www.terrapub.co.jp/journals/jjss/pdf/3702/37020299.pdf
Unfortunately, I don’t have an idea how to make the above square matrix have almost similar eigenvalues. Any help would be much appreciated.