September 17th, 2013, 12:13 PM  #1 
Newbie Joined: Sep 2013 Posts: 2 Thanks: 0  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 
September 17th, 2013, 12:27 PM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  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. 
September 17th, 2013, 12:36 PM  #3 
Newbie Joined: Sep 2013 Posts: 2 Thanks: 0  Re: Eigenvalue proof!
Just to be clear > rI where I is identity matrix Thank you for your fast reply. What is v? 
September 17th, 2013, 12:42 PM  #4  
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Eigenvalue proof! Quote:
I assume you know what eigenvalues and eigenvectors are?  

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