First, I appologise if this is in the wrong place, while the book is QM, the question is pure maths. Also I'm not sure if this techically counts as homework as I am self studying. Finally, sorry for the poor formatting, I'm not that good with LaTeX(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Given the matrix: [tex]\Omega[/tex] =

[tex]\left[ {\begin{array}{ccc}

2 & 0 & 0 \\

0 & 3 & -1 \\

0 & -1 & 3 \\

\end{array} } \right]

[/tex]

Show that [tex]\omega[/tex]_{1}= [tex]\omega[/tex]_{2}= 1; [tex]\omega[/tex]_{3}= 2

2. Relevant equations

3. The attempt at a solution

So det([tex]\Omega[/tex] - [tex]\omega[/tex]I) = (2 - [tex]\omega[/tex])((3 - [tex]\omega[/tex])(3 - [tex]\omega[/tex]) - 1)

Which obviously leaves [tex]\omega[/tex] = 2, but also (3 - [tex]\omega[/tex])^{2}= 1, the solutions to which should be [tex]\omega[/tex] = 2 and [tex]\omega[/tex] = 4.

Where am I going wrong?

Any help greatfully appreciated.

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# Finding eigenvalues, Shankar exercise 1.8.3

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