# Math Help - An interesting problem on C=A+B

1. ## An interesting problem on C=A+B

if A and B are symmetrical real matrices.
C=A+B

rc, ra, and rb are eigen values of C, A, and B.
I found that for the first several eigen values, they could be approximated as rc~=ra+rb. Is there any reason?

2. Originally Posted by chenuo
if A and B are symmetrical real matrices.
C=A+B

rc, ra, and rb are eigen values of C, A, and B.
I found that for the first several eigen values, they could be approximated as rc~=ra+rb. Is there any reason?

[b]If[/b ] A and B have the same eigenvectors, then the eigenvectors of C are the sums of corresponding egenvectors of A and B. "Corresponding" here meaning "for the same eigenvector". If $Av= \lambda_A v$ and $Bv= \lambda_B v$, then (A+B)v= Av+ Bv= \lambda_A v+ \lambda_B v= (\lambda_A+ \lambda_B)v[/tex].