Results 1 to 2 of 2

Thread: Eigen Space

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    10

    [Solved] Eigen Space

    $\displaystyle \begin{bmatrix}
    3 & 2\\
    4 & 1
    \end{bmatrix}$
    $\displaystyle det(A-\lambda I)=\begin{vmatrix}
    3-\lambda & 2\\
    4 & 1-\lambda
    \end{vmatrix}=(3-\lambda)(1-\lambda)-8=\lambda^2-4\lambda-5$
    $\displaystyle \lambda_{1}=5$ and $\displaystyle \lambda_{2}=-1$
    When $\displaystyle \lambda=5$, $\displaystyle \begin{bmatrix}
    -2 & 2\\
    4 & -4
    \end{bmatrix}\Rightarrow \begin{bmatrix}
    1 & -1\\
    0 & 0
    \end{bmatrix}$
    The eigenspace for$\displaystyle \lambda_{1}$ is $\displaystyle \begin{bmatrix}
    1\\
    1
    \end{bmatrix}$
    When $\displaystyle \lambda=-1$, $\displaystyle \begin{bmatrix}
    4 & 2\\
    4 & 2
    \end{bmatrix}\Rightarrow \begin{bmatrix}
    1 & \frac{1}{2}\\
    0 & 0
    \end{bmatrix}$
    The eigenspace for$\displaystyle \lambda_{2}$ is $\displaystyle \begin{bmatrix}
    1\\
    -2
    \end{bmatrix}$

    Solved nevermind
    Last edited by dwsmith; Apr 14th 2010 at 05:36 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,796
    Thanks
    3035
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding unit eigen values and eigen vectors
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Apr 11th 2011, 09:42 AM
  2. Complex Eigen Space
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: Apr 14th 2010, 08:09 PM
  3. Replies: 5
    Last Post: Apr 5th 2010, 02:41 AM
  4. Eigen space and probability question
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: Mar 2nd 2010, 05:54 AM
  5. find eigen value & space, urgent!
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Nov 27th 2007, 04:23 AM

Search Tags


/mathhelpforum @mathhelpforum