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Math Help - Diagonilizablity question

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    Diagonilizablity question

    Let A be an nxn matrix with eigenvalue ∆ with multiplicity n. Show that A is diagonizable iff A=∆I, where I is the nxn idenity.
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    Quote Originally Posted by Chris11 View Post
    Let A be an nxn matrix with eigenvalue ∆ with multiplicity n. Show that A is diagonizable iff A=∆I, where I is the nxn idenity.

    \Delta eigenvalue of A of multiplicity n\iff (x-\Delta)^n is the charateristic pol. of A , and thus A is diagonalizable \iff x-\Delta is the minimal pol. of A\iff A=\Delta I .

    Tonio
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    what is minimal pol?
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    The polynomial, p(x), of minimum degree such that p(A)v= 0 for all v in the vector space. Since every matrix satisfies its own characteristic equation, the minimal polynomial for a matrix must be a factor of the characteristic polynomial.
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