Exercise 1.1.23

Question

Create a 3 by 2 matrix $A$ with rank 1 . Factor $A$ into $A=C R$ and $A=C M R$.

Neil Z. · Accepted Answer

If we pick $$A=\begin{bmatrix}1 &2\2&4\3&6\end{bmatrix},$$ then we have
$$A=CR=\begin{bmatrix}1\2\3\end{bmatrix}\begin{bmatrix}1&2\end{bmatrix}.$$

We have $(C^TC)^{-1} = \frac{1}{14}$, and pick
$R=\begin{bmatrix}1&2\end{bmatrix}$, so $(RR^T)^{-1} = \frac{1}{5}$
and $C^TAR^T = 70$, so we have $M= \begin{bmatrix}1\end{bmatrix}$

Exercise 1.1.23

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Exercise 1.1.23

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