Solution
= Solution
If $A$ has full column rank, then for every nonzero $h$,
$$
h^TA^TAh=\|Ah\|^2>0.
$$
Thus $A^TA$ is positive definite and invertible, and the normal equation has the unique solution
$$
\boxed{c^*=(A^TA)^{-1}A^Ty.}
$$
= Solution
If $A$ has full column rank, then for every nonzero $h$,
$$
h^TA^TAh=\|Ah\|^2>0.
$$
Thus $A^TA$ is positive definite and invertible, and the normal equation has the unique solution
$$
\boxed{c^*=(A^TA)^{-1}A^Ty.}
$$