I am reading a research paper on linear quadratic control. https://arxiv.org/abs/1806.07104
I made my way until Algorithm 1 on section 5 where I am locked by a definition (?) I do not understand. Algorithm 1
This algorithm requires to compute a Frobenius norm projection onto a matrix at each time step.
I recall from my undergrad classes that the Frobenius norm of a matrix is defined as:
$\|A\|_F^2 = \text{Tr}(A^TA)=\Sigma_{i=1}^n\Sigma_{j=1}^n |a_{ij}|$
I also recall that a projection on a vector space is an application $p$ such that $p \circ p = p$ or $P^2 = P$ with $P$ the matrix representation of $p$.
But I have no idea how to compute a Frobenius norm projection on a matrix by hand.