Hi all,..I need help for this problem

Let A \in \mathbb{C}^{n \times n}.
Let S=\left[ <br />
\begin{array}{cc}<br />
I & 0 \\ <br />
0 & H%<br />
\end{array}%<br />
\right] \in <br />
%TCIMACRO{\U{2102} }%<br />
%BeginExpansion<br />
\mathbb{C}<br />
%EndExpansion<br />
^{n \times n}, where H is a k \times k Householder matrix such that SA has zero component in the first column, from line n - k + 2 to n.

Consider matrix B = SAS^{*} = SAS.
Check whether or not B has zero component in the first column, from line n - k + 2 to n.


I am still confused about the householder matrix H, is it a tridiagonal matrix? what are the properties?