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Math Help - 2x2 matrix - help needed!

  1. #1
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    2x2 matrix - help needed!

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    Last edited by JrShohin; October 18th 2008 at 09:57 AM.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by JrShohin View Post
    A matrix is positive definite if its eigenvalues are all positive.
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    Quote Originally Posted by Moo View Post
    Hello,

    A matrix is positive definite if its eigenvalues are all positive.
    That's all?
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    Quote Originally Posted by JrShohin View Post
    That's all?
    Well, if you know how to find the characteristic polynomial, then that's all

    The roots of the characteristic polynomial are the eigenvalues. So find \alpha such that there are indeed positive.

    Characteristic polynomial - Wikipedia, the free encyclopedia
    Positive-definite matrix - Wikipedia, the free encyclopedia (but I'm afraid this article may not correspond to your level...I can't tell)
    Let M be an n n [...] matrix. The following properties are equivalent to M being positive definite:
    1. All eigenvalues λi of M are positive. [...]
    That's the part you need.
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    Quote Originally Posted by Moo View Post
    Well, if you know how to find the characteristic polynomial, then that's all

    The roots of the characteristic polynomial are the eigenvalues. So find \alpha such that there are indeed positive.

    Characteristic polynomial - Wikipedia, the free encyclopedia
    Positive-definite matrix - Wikipedia, the free encyclopedia (but I'm afraid this article may not correspond to your level...I can't tell)

    That's the part you need.
    Thank you,

    to tell the truth, i'm just beginning linear algebra, and plus, i haven't worked on maths for a loooong time and i forgot...
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    Last edited by JrShohin; October 18th 2008 at 09:57 AM.
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    Quote Originally Posted by JrShohin View Post


    And how about this last one?
    Hmmm

    A diagonal 2x2 matrix is in the form \begin{pmatrix} \gamma & 0 \\ 0 & \delta \end{pmatrix}
    And the equivalent diagonal matrix to a given matrix will be formed by its eigenvalues. That is to say, in our case here, \gamma and \delta are the eigenvalues of A.

    Did you find them ?

    For the eigenvectors, it's better you have a look on the internet...
    Try this : Pauls Online Notes : Differential Equations - Review : Eigenvalues & Eigenvectors (it's also explain how to get the eigenvalues)
    Take the time to read it please
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