- #1
pyroknife
- 613
- 3
Homework Statement
$$\begin{bmatrix}
a_{11} & a_{12} & 0 & 0\\
a_{12} & a_{22} & a_{23} & 0\\
0 & a_{23} & a_{33} & a_{34} \\
0 & 0 & a_{34} & a_{44} \\
\end{bmatrix}
=
\begin{bmatrix}
q_{11} & q_{12} & q_{13} & q_{14} \\
q_{21} & q_{22} & q_{23} & q_{24} \\
q_{31} & q_{32} & q_{33} & q_{34} \\
q_{41} & q_{42} & q_{43} & q_{44} \\
\end{bmatrix}
\begin{bmatrix}
r_{11} & r_{12} & r_{13} & r_{14} \\
0 & r_{22} & r_{23} & r_{24} \\
0 & 0 & r_{33} & r_{34} \\
0 & 0 & 0 & r_{44} \\
\end{bmatrix}
$$
For the given 4x4 symmetric tridiagonal matrix A, determine which elements of its QR factorization is zero. The trick is to determine this visually.
Homework Equations
The Attempt at a Solution
I plugged a simple 4x4 symmetric tridagonal matrix into MATLAB and took its qr factorization and found that the top left element, ##r_{14}## of the matrix R and the bottom left 3 elements, ##q_{31}, q_{41}, q_{42}## of the matrix Q are zero. But the task was to determine this with ease and visually. Is there a trick to do this? I am not seeing it.