Solution
= Solution
The product identity always holds, since
$$
\prod_i\mu_i=\det(A^TA)=\det(A^T)\det A=(\det A)^2
=\left(\prod_i\lambda_i\right)^2.
$$
Therefore
$$
\boxed{\prod_{i=1}^n\mu_i=\prod_{i=1}^n\lambda_i^2}.
$$
= Solution
The product identity always holds, since
$$
\prod_i\mu_i=\det(A^TA)=\det(A^T)\det A=(\det A)^2
=\left(\prod_i\lambda_i\right)^2.
$$
Therefore
$$
\boxed{\prod_{i=1}^n\mu_i=\prod_{i=1}^n\lambda_i^2}.
$$