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Mathematics-Online problems:

Interactive Problem 3: Transformation into Diagonal Form

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Given the matrix

\begin{displaymath}A=\left( \begin{array}{rrr} -11 & 2 & 8 \\ 2 & -2 & 10 \\ 8 & 10 & -5 \end{array}\right). \end{displaymath}

Find an orthogonal matrix $ T$ in such a way that $ D={T}^{\operatorname t}AT$ is a diagonal matrix and declare $ D$ explicitly. The diagonal of $ T$ should consist of positive values and the diagonal of $ D$ should be sorted ascending.

Transform the entries of $ T$ into the common denominator $ 9$ and give the numerators:

$ T= \displaystyle\frac{1}{9}\left(\rule{0pt}{6ex}\right.$
$ \left.\rule{0pt}{6ex}\right)$

$ D= \left(\rule{0pt}{6ex}\right.$
0 0
0 0
0 0
$ \left.\rule{0pt}{6ex}\right)$

   

(Authors: Hörner/Höfert)

Solution:

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  automatically generated: 8/11/2017