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Use Lagrange's method to find the maximum value of $\langle A\mathbf{x},\mathbf{x}\rangle$ subject to condition $\langle \mathbf{x},\mathbf{x}\rangle=1$ and $\langle \mathbf{u}_1,\mathbf{x}\rangle =0$ where $\mathbf{u}_1$ is a non zero vector in $N(s_1^2I_n-A^TA)$, $s_1$ is the largest singular value of A and $A=A^T \in \mathbb{R}^{n\times n}$.

Can anybody please explain me how to proceed with this question?

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Maybe a stupid question, but what is $N(s_1^2I_n-A^TA)$ ? –  sonystarmap Jan 31 '13 at 13:31
Just a guess: the null space of the matrix $s_1^2 I_n - A^T A$? –  Siminore Jan 31 '13 at 15:00
N represents the null space –  aneps Jan 31 '13 at 18:50

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