trace(A) is the sum of the eigenvalues of $A$.


For matrix \(A \in \mathbb{R}^{m \times n}\)

  • 1-norm / max column sum: \(||A||_1 = \underset{1 \le j \le n}{\max} \sum_{i=1}^{m} | a_{ij} |\)

  • 2-norm / spectral norm: \(||A||_2 = (\rho(A^* A))^{1/2} = \sigma_{max}(A)\) , the larget eigenvalue of \(A^* A\), or larget singular value of \(A\). $A^*$ is the pseudo-inverse of $A$.

  • inf-norm / max row sum: \(||A||_\infty = \underset{1 \le i \le m}{\max} \sum_{j=1}^{n} | a_{ij} |\)

\(Z = W H^T\), where \(W \in \mathbb{R}^{d \times k}, H \in \mathbb{R}^{L \times k}\). \(\|Z\|_{tr} = \frac{1}{2} ( \|W\|_F^2 + \|H\|_F^2 )\).