grandes-ecoles 2021 Q3

grandes-ecoles · France · centrale-maths1__official Matrices Matrix Entry and Coefficient Identities

Show that $$\|A - B\|_{F}^{2} = \sum_{1 \leqslant i,j \leqslant n} p_{i,j}^{2} \left(\lambda_{i}(A) - \lambda_{j}(B)\right)^{2}.$$

Show that
$$\|A - B\|_{F}^{2} = \sum_{1 \leqslant i,j \leqslant n} p_{i,j}^{2} \left(\lambda_{i}(A) - \lambda_{j}(B)\right)^{2}.$$