Science:Math Exam Resources/Courses/MATH221/December 2009/Question 12 (e)
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Question 12 (e) 

Mark each statement either True or False. You do not have to justify your answer. e. If is the orthogonal projection onto a subspace W, then the standard matrix of T is diagonalizable. 
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Hint 

Science:Math Exam Resources/Courses/MATH221/December 2009/Question 12 (e)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. True. For a matrix to be diagnonizable, it must be able to be written in this form: where D is a matrix with the eigenvalues of A as its diagonal. All projection matrices to the same dimension are diagonizable. Since all vectors in W project onto itself with that transformation, the eigenvalues of T are 0 and 1, hence . 