LU factorisation
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Form an LU factorization of the following symmetric matrix to show that it is not positive definite.
4 1 -1 2
1 3 -2 -1
-1 -2 1 6
2 -1 6 1
Using a little ingenuity we can find a non-zero vector such as x^T = ( 0 1 1 0) that does not satisfy the requirement x^T Ax > 0.
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Solution Summary
This solution explains the steps to LU factorization and how to show that the matrix is not positive definite.
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