λi i=index zum Unterscheiden
\( |A- \lambda E|= \lambda^{2} - 2 \; ί \; \lambda - 5 = 0\)
===> \(\{\lambda_1 =2+i,\lambda_2 =-2+i\}\)
===>\(\small \left(\begin{array}{rrrr}λ=&2 + ί&\left(\begin{array}{rr}-2&2\\2&-2\\\end{array}\right)&\left(\begin{array}{r}x1\\x2\\\end{array}\right) = 0\\λ=&-2 + ί&\left(\begin{array}{rr}2&2\\2&2\\\end{array}\right)&\left(\begin{array}{r}x1\\x2\\\end{array}\right) = 0\\\end{array}\right)\)
===>\(\small \left(\begin{array}{r}x1\\x2\\\end{array}\right) = \left(\begin{array}{rr}x2&-x2\\x2&x2\\\end{array}\right)\)
ist Dir damit weiter geholfen?