Der Vollständigkeit halber
(nach https://de.wikipedia.org/wiki/Givens-Rotation)
\(\small M \, := \, \left(\begin{array}{rr}20&52\\0&15\\15&14\\\end{array}\right)\)
\(\small \left\{ m_{31} = 0, \left(\begin{array}{rrr}\frac{aii}{\sqrt{aii^{2} + aik^{2}} \; \operatorname{sgn}\left(aii \right)}&0&\frac{aik}{\sqrt{aii^{2} + aik^{2}} \; \operatorname{sgn}\left(aii \right)}\\0&1&0\\-\frac{aik}{\sqrt{aii^{2} + aik^{2}} \; \operatorname{sgn}\left(aii \right)}&0&\frac{aii}{\sqrt{aii^{2} + aik^{2}} \; \operatorname{sgn}\left(aii \right)}\\\end{array}\right),Q1:= \left(\begin{array}{rrr}\frac{4}{5}&0&\frac{3}{5}\\0&1&0\\-\frac{3}{5}&0&\frac{4}{5}\\\end{array}\right) \right\} \)
\(\small M1 \, := \, \left(\begin{array}{rr}25&50\\0&15\\0&-20\\\end{array}\right)\)
\(\small \left\{ m1_{32} = 0, \left(\begin{array}{rrr}1&0&0\\0&\frac{aii}{\sqrt{aii^{2} + aik^{2}} \; \operatorname{sgn}\left(aii \right)}&\frac{aik}{\sqrt{aii^{2} + aik^{2}} \; \operatorname{sgn}\left(aii \right)}\\0&-\frac{aik}{\sqrt{aii^{2} + aik^{2}} \; \operatorname{sgn}\left(aii \right)}&\frac{aii}{\sqrt{aii^{2} + aik^{2}} \; \operatorname{sgn}\left(aii \right)}\\\end{array}\right), Q2:=\left(\begin{array}{rrr}1&0&0\\0&\frac{3}{5}&-\frac{4}{5}\\0&\frac{4}{5}&\frac{3}{5}\\\end{array}\right) \right\} \)
Q2 Q1 M =\(\small R \, = \, \left(\begin{array}{rr}25&50\\0&25\\0&0\\\end{array}\right)\)
und um zu testen ob GeoGebra richtig tut...
