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Topic: eigenvalues of A
Replies: 4   Last Post: Nov 4, 2009 11:25 PM

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Arturo Magidin

Posts: 786
Registered: 8/24/06
Re: eigenvalues of A
Posted: Nov 4, 2009 11:25 PM
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On Nov 4, 9:48 pm, G Patel <gaya.pa...@gmail.com> wrote:
> On Nov 4, 9:56 pm, G Patel <gaya.pa...@gmail.com> wrote:
>

> > true or false.... eigenvalues of A are same as eigenvalues of kA
> > (because if v is eigenvector for A, then kv is eigenvector for kA)

>
> if c is eigenvalue of A, then Ax = cx for nonzero x, multiply both
> sides by nonzero scalar k: (kA)x = c(kx) , thus c is also eigenvalue
> of kA?


An eigenvalue of A is a scalar c such that there exists a nonzero
vector x for which Ax=cx.

Note that the vector on the left side of "Ax=cx" is the *same* as the
vector on the right side of "Ax=cx".

Question: is the vector on the left side of your "(kA)x = c(kx)" the
same as the vector on your right hand side?

And to put it even more plainly, *again*:

What are the eigenvalues of, say, the identity matrix?

What are the eigenvalues of k times the identity?

PS: You are utterly confused; go talk to your professor because you
are just not getting this.

--
Arturo Magidin



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