johnnyb

Suppose that A is an n x n matrix with eigenvalues ?1,..., ?n.

Let B=A + rI where r is an arbitrary scalar. Prove that the eigenvalues of B are: (?1 + r),...,( ?n + r)

If anyone has ideas, any help appreciated

Pero

For matrices A and B and vector v, you have:

(A+B)v = Av + Bv

Maybe you can take it from there.

johnnyb

Just to be clear -> rI where I is identity matrix

Thank you for your fast reply. What is v?

Pero

v is a vector. And A and B are any matrices. Maybe I should have used X and Y to avoid confusion.

I assume you know what eigenvalues and eigenvectors are?