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Math Help - eigenvalues

  1. #1
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    eigenvalues

    1. Let A be nxn matrix, suppose that <br />
A \ne 0,I,A^2  = A<br />
so prove that <br />
\lambda  = 1,\lambda  = 0<br />
are eigenvalues.

    2. if I know that A and B are similar how can I find P invertibale that sustains: <br />
B = P^{ - 1} AP<br /> <br />
?
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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 <br />
A \ne 0,I,A^2  = A<br />
so prove that <br />
\lambda  = 1,\lambda  = 0<br />
are eigenvalues.
    Ax = \lambda x \implies A^2 x = \lambda Ax = \lambda ^2 x But A^2 = A \implies \lambda x = Ax = \lambda ^2 x. This means \lambda^2 = \lambda

    2. if I know that A and B are similar how can I find P invertibale that sustains: <br />
B = P^{ - 1} AP<br /> <br />
?
    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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