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um nochmal meine frage zu formulieren
wenn die Matrix A den eigenvektor x hat
hat die matrix r*A (r aus R\{0})
die selben eigenvektoren?
ich denke ja:
A*x=L*x | *r r*(A*x)=r*(L*x) |assoziativ (r*A)*x=(r*L)*x
Es verändern sich also nur die Eigenwerte