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?
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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?
Expect your answers!
[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 and , then (A+B)v= Av+ Bv= \lambda_A v+ \lambda_B v= (\lambda_A+ \lambda_B)v[/tex].
Otherwise, I don't know how you are going to choose which eigenvalues of A and B to add to get eigenvalues of B.