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Math · Advanced Math
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The symmetric matrix -35 -15 -15 5 has two distinct eigenvalues \lambda _{1} < \lambda _{2} .

I've figured out that they are: \lambda _{1} = -40 ; \lambda _{2} = 10 .

How do I get p_{1}   and p_{2} of \mathit{P} = [p_{1}\; p_{2}] to achieve \mathit{P}^{\textup{T}}\mathit{AP} = \begin{bmatrix} \lambda _{1} & \\ & \lambda _{2} \end{bmatrix} ?

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