hwA-alt - Assignment #10-alt: Matrix Factorization and...

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Assignment #10-alt: Matrix Factorization and Matrix Norms Due date: Wednesday, November 24, 2010 (10:10am) For full credit you must show all of your work. 1. Consider the matrix A = 4 " 12 8 " 12 40 " 28 8 " 28 29 # $ % % % ( ( ( . a. Derive the factorizations listed below. You may use results from your earlier factorizations (e.g. 1a) in your answers for the later factorizations. i. A = LU where L is unit lower triangular, and U is upper triangular (Doolittle factorization) ii. A = LU where L is lower triangular, and U is unit upper triangular (Crout factorization) iii. A = LDU where L is unit lower triangular, D is diagonal, and U is unit upper triangular iv. A = LL T where L is lower triangular (Cholesky factorization) b. Using your answers above where applicable, calculate the magnitude of the determinant of matrix A. [Hint: if A = LDU , det( A ) = det( L ) det( D ) det( U ). Also, det( A T ) = det( A ), and the determinant of a lower triangular matrix is given by the product of its diagonal elements.] 2. Give an example of a symmetric matrix that does not have an
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hwA-alt - Assignment #10-alt: Matrix Factorization and...

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