- #1
Haorong Wu
- 415
- 90
Homework Statement
Diagonalize the matrix $$ \mathbf {M} =
\begin{pmatrix}
1 & -\varphi /N\\
\varphi /N & 1\\
\end{pmatrix}
$$ to obtain the matrix $$ \mathbf{M^{'}= SMS^{-1} }$$
Homework Equations
First find the eigenvalues and eigenvectors of ##\mathbf{M}##, and then normalize the eigenvectors to get ##\mathbf{S^{-1}}##.
The Attempt at a Solution
After calculation, the eigenvalues are ## \lambda = 1 \pm \frac \varphi N##, and the corresponding eigenvectors (unnormalized) are ##\begin{pmatrix}
i \\ 1
\end{pmatrix}## and ##
\begin{pmatrix}
-i \\1
\end{pmatrix}
##.
Then I try to Schmidt them, but I failed to normalize them.
Could you help me normalize them?
Regards