1. The problem statement, all variables and given/known data Hey guys, for my linear algebra class I need to find the signs of the eigenvalues (I just need to know how many are positive and how many are negative) of an nxn matrix with zeros everywhere except for the two diagonals directly above and directly below the main diagonal, which both have all entries 1/2. Here's a picture with n=10: http://img249.imageshack.us/img249/9405/10x10lo9.png [Broken] http://g.imageshack.us/img249/10x10lo9.png/1/ [Broken] 2. Relevant equations 3. The attempt at a solution I know that I can take teh determinant and solve the characteristic equation, but I don't know how I would do that for an nxn matrix. Also, it seems like it shouldn't require so much work, since I need to know their signs but not their values. Can anybody point me in the right direction?