On Nov 22, 2007, at 11:13 PM, Saba Tehrani wrote: > Hi everybody > > I want to find the eigenvalues and eigenvectors of a 4by4 matrix > (this matrix is equal to it's inverse). Can anybody guid me how I can > start? I searched alot but I didn't find anything for this kind of > matrix. > > Cheers > Saba
It has been a while since I dabbled with this stuff (like 13 years), but you have Ax=vx and also AA^-1=A^-1A=I, where I is the identity matrix, x is an eigenvector and v is an eigenvalue. You also have AAx=vAx or Ix=vAx or x=vAx=v^2x. If this is to hold for all eigenvectors, v^2=1, so v=+1 or v=-1. Then you have to solve Ax=-x and Ax=x or (A+I)x=0 and (A-I)x=0, you probably have the routines for that. If not LU-decomposition and backsubstitution (you can find them in Press et all) are quick to implement. cheers, Jacob
