Re: ? what is the x maximizing norm(b) where b = A*x


"Robert Israel" <israel@xxxxxxxxxxx> wrote in message
news:dmnunh$2er$1@xxxxxxxxxxxxxxxxxxxxxxxxx
>
> Hint: a self-adjoint matrix has an orthonormal basis of eigenvectors.
> Calculate the norm of Ax if x is a linear combination of these basis
> vectors.
>

I knew the expression of A*x can be

A*x = V*D*V'*x = sum( ( landa(n)*v(n)'*x )*v(n), n = 1,...N ),

v(n) are e-vectors and landa(n) are e-values.

and that's why I guessed the e-vector corresponding to the max

e-value might be the answer. But did not see why.

Thanks,
by Cheng Cosine
Dec/01/2k5 NC


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