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Thread: eigenvalues

  1. #1
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    eigenvalues

    1. Let A be nxn matrix, suppose that $\displaystyle
    A \ne 0,I,A^2 = A
    $ so prove that $\displaystyle
    \lambda = 1,\lambda = 0
    $ are eigenvalues.

    2. if I know that A and B are similar how can I find P invertibale that sustains: $\displaystyle
    B = P^{ - 1} AP

    $?
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  2. #2
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    Quote Originally Posted by omert View Post
    1. Let A be nxn matrix, suppose that $\displaystyle
    A \ne 0,I,A^2 = A
    $ so prove that $\displaystyle
    \lambda = 1,\lambda = 0
    $ are eigenvalues.
    $\displaystyle Ax = \lambda x \implies A^2 x = \lambda Ax = \lambda ^2 x$ But $\displaystyle A^2 = A \implies \lambda x = Ax = \lambda ^2 x$. This means $\displaystyle \lambda^2 = \lambda$

    2. if I know that A and B are similar how can I find P invertibale that sustains: $\displaystyle
    B = P^{ - 1} AP

    $?
    Isnt that the definition?
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  3. #3
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    Quote:
    2. if I know that A and B are similar how can I find P invertibale that sustains: ?
    Isnt that the definition?
    I wanted to know, that in case that I know A and B, and I know that they are similar, how can I find P
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