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johnnyb September 17th, 2013 11:13 AM

Eigenvalue proof!
 
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 September 17th, 2013 11:27 AM

Re: Eigenvalue proof!
 
For matrices A and B and vector v, you have:

(A+B)v = Av + Bv

Maybe you can take it from there.

johnnyb September 17th, 2013 11:36 AM

Re: Eigenvalue proof!
 
Just to be clear -> rI where I is identity matrix

Thank you for your fast reply. What is v?

Pero September 17th, 2013 11:42 AM

Re: Eigenvalue proof!
 
Quote:

Originally Posted by Pero
For matrices A and B and vector v, you have:

(A+B)v = Av + Bv

Maybe you can take it from there.

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?


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