Symmetrische Matrizen haben bekannterweise(?) relle EW:
https://www.geogebra.org/m/BpqJ28eP#material/upUZg79r
A:= {{-1,0,0,-2 ί },{0,-1,2 ί ,0},{0,-2 ί ,-1,0},{2 ί ,0,0,-1}}
|A - λ id| = (λ−1)2(λ+3)2=0
⎝⎜⎜⎜⎜⎜⎜⎜⎜⎜⎛λ=λ=−31⎝⎜⎜⎛2002i02−2i002i20−2i002⎠⎟⎟⎞⎝⎜⎜⎛−2002i0−2−2i002i−20−2i00−2⎠⎟⎟⎞⎝⎜⎜⎛x1x2x3x4⎠⎟⎟⎞=0⎝⎜⎜⎛x1x2x3x4⎠⎟⎟⎞=0⎠⎟⎟⎟⎟⎟⎟⎟⎟⎟⎞
⎝⎜⎜⎛x1x2x3x4⎠⎟⎟⎞=⎝⎜⎜⎛ix4−ix3x3x4−ix4ix3x3x4⎠⎟⎟⎞
S : =⎝⎜⎜⎜⎛2i002102−i21002i2102−i0021⎠⎟⎟⎟⎞