hwA-alt

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online