Da löst sich nix auf, man erhält
(A - λ E)=0
\(\small \left(\begin{array}{rrrr}\lambda=&-\sqrt{a}&\left(\begin{array}{rr}\sqrt{a}&1\\a&\sqrt{a}\\\end{array}\right)&\left(\begin{array}{r}x1\\x2\\\end{array}\right) = 0\\\lambda=&\sqrt{a}&\left(\begin{array}{rr}-\sqrt{a}&1\\a&-\sqrt{a}\\\end{array}\right)&\left(\begin{array}{r}x1\\x2\\\end{array}\right) = 0\\\end{array}\right) \)
\(\small \left(\begin{array}{rr}\sqrt{a} \; x1 + x2=0&a \; x1 + \sqrt{a} \; x2=0\\-\sqrt{a} \; x1 + x2=0&a \; x1 - \sqrt{a} \; x2=0\\\end{array}\right)⇒ \, \left(\begin{array}{rr}-\sqrt{a} \cdot \frac{x2}{a}&x2\\\sqrt{a} \cdot \frac{x2}{a}&x2\\\end{array}\right), x2∈ℝ \)
x2=1 ==> \(\small T \, := \, \left(\begin{array}{rr}-\frac{\sqrt{a}}{a}&\frac{\sqrt{a}}{a}\\1&1\\\end{array}\right)\)
\( \small D:=T^{-1} A\; T= \, \left(\begin{array}{rr}-\sqrt{a}&0\\0&\sqrt{a}\\\end{array}\right)\)
