I'm reading another definition of $PCA$, quite different from what I've been used to see and I'm a little bit confused:
given a dataset $X \in \mathbb{R}^{d \times m}$ that we approximate as $X \sim V^TA$ by minimizing the following loss wrt to the constraints $A \in \mathbb{R}^{l \times m}, \, V \in \mathbb{R}^{l \times d}\, , \, VV^T = \mathbb{I}_l$:
$$\mathcal{L}_{pca}(X; A, V) = \|X - V^TA\|^2_F$$
What do matrices $A,V$ represent here? And why is it used the Frobenius norm?
Many thanks,
James