#eigendecomposition

Question 1: Single choice

A symmetric matrix $A$ has eigendecomposition $A = U\Sigma U^\top$ . Which matrix is its projection onto the set of positive semidefinite matrices, i.e. the PSD matrix closest to $A$ in Frobenius norm?

$U|\Sigma|U^\top$ , where $|\Sigma|$ flips the sign of the negative eigenvalues1
$U\Sigma_+U^\top$ , where $\Sigma_+$ sets the negative eigenvalues to 02
$A$ with its negative entries set to 03
$A + |\lambda_{\min}|\,I$ , which shifts every eigenvalue up4

Timed test