# Basics

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

# Norm

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