Re: Alternative Eigenvalue Problem

On Nov 7, 8:39 am, Alois Steindl <Alois.Stei...@xxxxxxxxxxxx> wrote:
jonathan.eth...@xxxxxxxxx writes:
Hi Everyone,

Consider the typical eigenvalue problem [A][v] = b[v] where [A] is an
NxN matrix, [v] is an Nx1 vector and b is a constant.

I was wondering about the following problem: [A][v] = [D][v] where
everything is the same as before, only now [D] is a diagonal NxN
matrix.

Is there a way to solve for a collection of diagonal matrices [D] and
vectors [v] in the same manner as the usual eigenvalue problem?

Thanks for your time,
-Jon

Hello,
I am not sure about the background for this example.

As stated, it looks quite trivial to me: Given any matrix A and vector
v (with no vanishing component), you should be able to find a diagonal
matrix D, such that Av=Dv, just by taking D_{ii} = (Av)_i/v_i.

Alois

Hi Alois,

Thanks for replying.

The idea is we don't know the vector v or diagonal matrix D, just the
fully populated A.

[A][v] = b[v] is analogous to [A][v] = [D][v]. That's how it seems
similar (from my POV) to an eigenvalue problem.

.

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