Exercise Solution 2.10

  1. The Cholesky algorithm yields the matrix

    [s1]

    Because the algorithm completes successfully with no 0 diagonal elements, the original matrix is positive definite.

  2. At the fifth step of the Cholesky algorithm, we obtain

    [s2]

    where x is indeterminate. We set x equal to 0 and proceed. We obtain the matrix

    [s3]

    Because this has a 0 diagonal element, we conclude that the original matrix is singular positive semidefinite.

  3. The Cholesky algorithm fails. The matrix is neither positive definite nor singular positive semidefinite.

 

Welcome!

Enter your address for insights that will transform your risk management.

Click the link in the email I just sent you to confirm your address and start your subscription.

Defining Risk

Enter your email address to receive your copy and subscribe to Glyn's Risk Management Newsletter.

Click the link in the email I just sent you to download your paper and start your subscription.