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September 17th, 2013, 12:13 PM   #1
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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, 12:27 PM   #2
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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, 12:36 PM   #3
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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, 12:42 PM   #4
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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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