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hitmeoff
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Homework Statement
Suppose the A [tex]\in[/tex] Mn X n(F) has two distinct eigenvalues, [tex]\lambda[/tex]1 and [tex]\lambda[/tex]2, and that dim(E[tex]\lambda[/tex]1) = n -1. Prove A is diagonalizable.
Homework Equations
The Attempt at a Solution
1. The charac poly clearly splits because we have eigenvalues.
2. need to show m = dim (E).
Ok, we are given that dim(E[tex]\lambda[/tex]1) = n - 1
we know multiplicity has to be 1 [tex]\leq[/tex] dim(E[tex]\lambda[/tex]1) [tex]\leq[/tex] m.
so: 1 [tex]\leq[/tex] n - 1 [tex]\leq[/tex] m.
But I am stuck now, not sure how to show that m = dim(E[tex]\lambda[/tex])
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