0
Moin,
gegeben sind drei Eigenvektoren:
\[ \begin{pmatrix} -1 \\ \sqrt{2} \\ 1 \end{pmatrix} \] \[ \begin{pmatrix} -1 \\ -\sqrt{2} \\ 1 \end{pmatrix} \]\[ \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} \]
und deren Beträge:
\[ 2, 2, \sqrt{2} \]
Die Drehmatrix ergibt sich nun aus:
\[ Betrag \cdot Eigenvektor \]
Im Skript ist als Lösung:
![](data:image/png;base64,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)
angegeben.
Das kann doch nicht sein, weil \[ \frac 1 2 \cdot \sqrt{2} \neq 1 \].
Wobei \[ \frac 1 2\] hier der Kehrwert des Betrags von den ersten beiden Eigenvektoren ist.
gegeben sind drei Eigenvektoren:
\[ \begin{pmatrix} -1 \\ \sqrt{2} \\ 1 \end{pmatrix} \] \[ \begin{pmatrix} -1 \\ -\sqrt{2} \\ 1 \end{pmatrix} \]\[ \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} \]
und deren Beträge:
\[ 2, 2, \sqrt{2} \]
Die Drehmatrix ergibt sich nun aus:
\[ Betrag \cdot Eigenvektor \]
Im Skript ist als Lösung:
angegeben.
Das kann doch nicht sein, weil \[ \frac 1 2 \cdot \sqrt{2} \neq 1 \].
Wobei \[ \frac 1 2\] hier der Kehrwert des Betrags von den ersten beiden Eigenvektoren ist.
Diese Frage melden
gefragt
anonym2d7d2
Punkte: 12
Punkte: 12