Please explain what results we use to get the following:
$$\|AA^T(Ax-b)\| \leq \|A^TA\|\cdot\|(Ax-b)\|,$$
where $A$ is an $m \times n$ matrix; $b$ and $x$ are $m \times 1$ vectors, and $\|.\|$ is the $2$-norm.
Please explain what results we use to get the following:
$$\|AA^T(Ax-b)\| \leq \|A^TA\|\cdot\|(Ax-b)\|,$$
where $A$ is an $m \times n$ matrix; $b$ and $x$ are $m \times 1$ vectors, and $\|.\|$ is the $2$-norm.