Homework #5. Due February 12 |

Problems u.* are from the Review of Chapter u, prblems u.x.* are from section x in chapter u.

Part A: 3.14, 3.18, 3.28, 3.39, 4.2.1, 4.2.10

Part B: Strang 3.4.5, 3.4.8, 3.4.14, 3.4.18, 3.4.21, 3.4.22, 4.2.6, 4.2.14

and the following problem:

9. Cholesky factorization.

Suppose A is invertible.

a. Show that a symmetric (real) matrix A can be represented (factorized) into

A= L D L

b. Suppose the diagonal matrix D has nonnegative values on the diagonal. Then we can define D

c. Let S=L D

d. Show (using Gram-Schmidt) that if B = A