[tex] A = \[ \left( \begin{array}{ccc}(adsbygoogle = window.adsbygoogle || []).push({});

0 & 0 & 1 \\

0 & 1 & 0 \\

1 & 0 & 0 \end{array} \right)\] [/tex]

eigenvalues are [tex] \lambda_{1} = -1, \ \lambda_{2} = \lambda_{3} = 1 [/tex]

[tex](A-\lambda_{1}I)u^{(1)} = 0 \ => \ u^{(1)} = \[ \left( \begin{array}{c}

-1 \\

0 \\

1 \end{array} \right)\] [/tex]

[tex] (A-\lambda_{2}I)u^{(2)} = 0 \ => u^{(1)} = \[ \left( \begin{array}{c}

1 \\

0 \\

1 \end{array} \right)\] [/tex]

[tex] (A -\lambda_{3}I)u^{(3)} = u^{(2)} \ => \

\left(

\begin{array}{ccc|c}

1&0&-1&-1\\

0&0 &0&1\\

0&0&0&0

\end{array}

\right)

[/tex]

since we cannot have 0 = 1, we can say that there is only one eigenvector for

[tex]\lambda = 1 [/tex]

which means that the Jordan form will be

[tex] \[ \left( \begin{array}{ccc}

1 & 1 & 0 \\

0 & 1 & 0 \\

0 & 0 & -1 \end{array} \right)\] [/tex]

Am I correct?

Now I need to find exp(Jt) and I'm not sure how.

If I only have 2 eigenvectors, how can I find the fund. matrix T such that

[tex]e^{At} = Te^{Jt}T^{-1} [/tex]?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Matrix exponentials

Loading...

Similar Threads for Matrix exponentials |
---|

I Eigenproblem for non-normal matrix |

A Eigenvalues and matrix entries |

A Badly Scaled Problem |

I Adding a matrix and a scalar. |

I Matrix exponential |

**Physics Forums | Science Articles, Homework Help, Discussion**