(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A be a symmetric n x n - matrix with eigenvalues and orthonormal eigenvectors [tex](\lambda_k, \xi_k)[/tex] assume ordening: [tex] \lambda_1 \leq...\leq \lambda_n [/tex]

We define the rayleigh coefficient as:

[tex]

R(x) = \frac{(Ax)^T x}{x^T x}

[/tex]

Show that the following constrained problem produces the second eigenvalue and its eigenvector:

[tex]

min \left( R(X)| x \neq 0, x \bullet \xi_1 = 0 \right)

[/tex]

3. The attempt at a solution

In the first part of the exercise I was asked to proof that (without that inproduct being zero) the minimalisation produces the first eigenvalue. The idea was to use lagrange multipliers but I don't how to use it here.

Do I need to use Lagrange multipliers?

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# Homework Help: Rayleigh quotient

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