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@@ -172,7 +172,7 @@ Weitere Begriffe und Eigenschaften |
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(Qx, Qy)_2 &= (x, \overline{Q}^TQ y)_2 = (x,y)_2\\ |
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\norm{Qx}_2^2 &= (Qx, Qx)_2 = (x,x)_2 = \norm{x}_2^2\\ |
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\norm{Q}_2 &= \sup\limits_{\norm{x}_2 =1} \norm{Qx}_2 = \sup\limits_{\norm{x}_2 =1} \norm{x}_2 = 1\\ |
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\norm{Q^{-1}}_2 &= \sup\limits_{\norm{x}_2 =1} \norm{Q^{-1}x}_2 = \sup\limits_{\norm{x}_2 =1} \norm{\overline{Q}Q^{-1}x}_2 = \sup\limits_{\norm{x}_2 =1} \norm{x}_2 = 1 |
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\norm{Q^{-1}}_2 &= \sup\limits_{\norm{x}_2 =1} \norm{Q^{-1}x}_2 = \sup\limits_{\norm{x}_2 =1} \norm{QQ^{-1}x}_2 = \sup\limits_{\norm{x}_2 =1} \norm{x}_2 = 1 |
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\end{align*} |
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\end{enumerate} |
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\end{proof} |
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