Let \( A \in \mathbb{C}^{n \times n} \). Then the Frobenius norm is defined by

\[ \| A \|_F = \left( \sum_{i,j=1}^n |a_{ij}|^2 \right)^{1/2}. \]
Remarks
  • The Frobenius norm is sub-multiplicative.
  • The Frobenius norm is consistent with the Euclidean norm.