Mathematica and square roots

*To*: mathgroup at smc.vnet.net*Subject*: [mg125448] Mathematica and square roots*From*: Konstantin <kparchevsky at gmail.com>*Date*: Wed, 14 Mar 2012 00:39:42 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Dear All! I am new to this group. May be this question was already discussed, but I did not find solution, searching this group. I was calculating eigenvalues {x} and eigenvectors {v} of a square matrix A. The characteristic polynomial looks like (x^2 - a^2) (...) = 0 Command Eigenvalues[A] gives me eigenvalues x1 = +a; x2 = -a; x3 = ... Command Eigenvectors[A] gives corresponding eigenvectors. The problem is that 'a' in my computations can be both negative and positive. So, eigenvalues x1 and x2 can be either negative or positive depending on sign 'a'. It is much more convenient for further computations to have eigenvalues of fixed sign. I want my eigenvalues look like x1 = +Abs[a]; x2 = -Abs[a]; x3 = ... And, of course, I want to have corresponding eigenvectors. Is it possible to do this using Eigenvalues and Eigenvectors, or I have to solve equation A v = Abs[a] v "manually" to find eigenvector 'v' which corresponds to the eigenvalue Abs[a]? Thank you in advance.