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September 17th, 2013, 11:13 AM | #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 ![]() |
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September 17th, 2013, 11:27 AM | #2 |
Senior Member Joined: Jun 2013 From: London, England Posts: 1,312 Thanks: 115 | 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. |
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September 17th, 2013, 11:36 AM | #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? |
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September 17th, 2013, 11:42 AM | #4 | |
Senior Member Joined: Jun 2013 From: London, England Posts: 1,312 Thanks: 115 | Re: Eigenvalue proof! Quote:
I assume you know what eigenvalues and eigenvectors are? | |
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