In constructing a Householder matrix to zero out the last n l of a vector x in Rn, the scalar a must satisfy x 2 Instead of always taking a x 2 it is customary to choose a x 2 whenever x1 0 Explain the advantages of choosing a in this manner ...

In constructing the Householder matrix ...

In constructing a Householder matrix to zero out the last n - l of a vector x

Question:

In constructing a Householder matrix to zero out the last n - l of a vector x in Rn, the scalar a must satisfy |α| = ||x||2. Instead of always taking a = ||x||2. it is customary to choose a = -||x||2 whenever x1 > 0. Explain the advantages of choosing a in this manner.