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Math Help - question regarding complex eigen values.

  1. #1
    Junior Member pirateboy's Avatar
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    Portland, OR
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    question regarding complex eigen values.

    Ok, so I've read this

    http://www.mathhelpforum.com/math-he...tml#post356455

    But I'm still a bit confused.

    My question is this: How do I know when to use \lambda vs \bar{\lambda} to solve.

    Here's an example.

    x'_1 = 2x_1-5x_2

    x'_2=4x_1-2x_2

    So i take
    0=\begin{vmatrix}2-\lambda &-5\\ 4 &-2-\lambda \end{vmatrix}

    (skip a few steps)
    (some quadratic magic)
    *poof*

    \lambda = \pm 4i

    Ok, so now, how do I know which is my \lambda which is my \bar{\lambda}?
    Which one do I use to grind through the rest of this?
    Does it matter?

    If I solve the matrix for the zero vector using \lambda = 4i, I wind up with the vector \begin{bmatrix}5\\ 2-4i\end{bmatrix}.

    With \lambda = -4i, however, I get \begin{bmatrix}5\\2+4i\end{bmatrix}.

    Given initial conditions, this will effect my result, correct? But it only changes the signs of my constants. Which would be expected since the sign of the equations I end up will will also be opposite?


    (sorry if this is a stupid question)
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  2. #2
    Junior Member
    Joined
    Nov 2009
    Posts
    69

    Re: question regarding complex eigen values.

    It doesn't matter whether you work with 4i or -4i. You will wind up with the same set of solutions regardless. Try making up initial conditions and working the problem both ways. You will wind up with the same particular solution either way if you don't make any mistakes.
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