sol67 - Partial Solution Set, Leon 6.7 6.7.1 For each of...

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Partial Solution Set, Leon § 6.7 6.7.1 For each of the following, compute the determinants of all of the leading principal submatrices and use them to determine whether the matrix is positive definite. (In other words, compute the leading principal minors.) 1. A = ± 2 - 1 - 1 2 ² . Leading principal minors are 2 and 3; positive definite. 2. A = ± 3 4 4 3 ² . Leading principal minors are 3, - 7; not positive definite. 3. A = 6 4 - 2 4 5 3 - 2 3 6 . Leading principal minors are 6, 14, - 38; not positive definite. 4. A = 4 2 1 2 3 - 2 1 - 2 5 . Leading principal minors are 4, 8, and 13; positive definite. 6.7.5 For each of the following, find the Cholesky decomposition A = BB T , where B is a lower triangular matrix. (Problem 6.7.4 is to find factorizations of the form LDL T , which is an intermediate step here.) 1. A = ± 4 2 2 10 ² . (d) A = 9 3 - 6 3 4 1 - 6 1 9 .
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This note was uploaded on 07/17/2011 for the course MATH 311 taught by Professor Anshelvich during the Spring '08 term at Texas A&M.

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sol67 - Partial Solution Set, Leon 6.7 6.7.1 For each of...

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