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Unformatted text preview: is a linear transformation, ² = ( ³ 1, ⋯ ³ ´ ) is a basis for V, µ = ( ? 1, ⋯ ? ´ ) is a basis for W ° = ?¶ ² µ = · [ ?¸³ 1 ¹ ] µ ⋯ [ ?¸³ ´ ¹ ] µ º In » 2 ( ¼ ) : ? 2 − 2 ? + 3 ¶ ( ? 2 , ? ,1) = ½ 1 − 2 3 ¾ ? 2 − 2 ? + 3 ¶ (1, ? , ? 2 ) = ½ 3 − 2 1 ¾ ? 2 − 2 ? + 3 ¶ ( ? 2 , ? ,3) = ½ 1 − 2 1 ¾ Coordinates depend on choice of basis! D: » 3 ( ¼ ) → » 2 ( ¼ ) (Differentiation) ² = ( ? 3 , ? 2 , ? , 1) µ = ( ? 2 , ? , 1) ¿¶ ² µ = ¿¶ ( ? 3 , ? 2 , ? ,1) ( ? 2 , ? ,1) = À [ ¿¸? 3 ¹ ] µ [ ¿¸? 2 ¹ ] µ [ ¿¸?¹ ] µ [ ¿¸ 1 ¹ ] µ Á = À [3 ? 2 ] µ [2 ? ] µ [1] µ [0] µ Á = Â 3 2 1 Ã ? Ä : ¼ 2 → ¼ 2 ? Ä ¶ Å 1 , Å 2 Å 1 , Å 2 = Æ cos Ä − sin Ä sin Ä cos Ä Ç...
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 Fall '10
 ChristinaSaleh
 Linear Algebra, Algebra, Transformations, Vector Space, basis, Linear map

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