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Mathematics-Online problems:

Interactive Problem 75: Jordan Form of a Matrix

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 real matrix

$\displaystyle A=\left(\begin{array}{rrrr} 2 & 0 & 0 & 1 \\ 0 & 0 & -1 & 0 \\ -1 & 0 & 1 & -1 \\ 0 & 1 & 1 & 1 \end{array} \right). $

Find the Jordan canonical form $ J$ of $ A$. Start with the greatest Jordan block:

$ J= \left(\rule{0pt}{9ex}\right.$
0 0
0 0
0 0
0 0 0
$ \left.\rule{0pt}{9ex}\right)$ .

Complete the following matrix product, using $ 1$ or $ -1$, so that $ T$ transforms $ A$ into Jordan form, i.e. $ T^{-1}AT=J$ holds:

$ T= \left(\rule{0pt}{10ex}\right.$
$ 1$ $ 1$ $ 1$ $ 1$
$ \left.\rule{0pt}{9ex}\right)$ $ \left(\rule{0pt}{9ex}\right.$
$ 8$ 0 0 0
0 $ 4$ 0 0
0 0 $ 2$ 0
0 0 0 $ 1$
$ \left.\rule{0pt}{10ex}\right)$ .

   
(Authors: Hertweck/Höfert)

see also:

  automatically generated: 8/11/2017