Math 6420 • PDE

Given a set of linearly independent vectors
\(u_1,u_2,\ldots,u_n\)
\begin{enumerate}
\item[(a)] Describe the Gram-Schmidt procedure to produce an orthogonal set of vectors
from the original set.
\item[(b)] Suppose \(U\) is a matrix with linearly independent columns. Describe the \(QR\)
factorization of \(U\) using Householder transformations.
\item[(c)] In what sense are these two procedures equivalent? Prove your answer.
\end{enumerate}