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Unformatted text preview: 1 + d 2 + ··· d m elements in this list. 5. Theorem : The sequence β is automatically linearly independent. The matrix A is diagonalizable if and only if d 1 + ··· d r = n , and this is true if and only if d i = m i for all i . If this is the case, β is a basis for R n , and the matrix S whose columns are the vectors in β vectors satisﬁes AS = SD , with D diagonal. Note: Each d i ≥ 1, so if all the roots of f A ( X ) are distinct, then m = n , each d i = 1, ∑ d i = n , and A is automatically diagonalizable....
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This note was uploaded on 02/02/2011 for the course MAE 107 taught by Professor Tsao during the Spring '06 term at UCLA.
- Spring '06