# Convergence of sequences of matrices

Matrix converge? says that "$$A_n$$ converges to $$A$$ means that for some matrix norm, $$\left\lVert A_n−A\right\rVert \to 0$$. Equivalently, it means that every entry of $$A_n$$ converges to the corresponding entry of $$A$$." Why are these equivalent (how can it be proved)?

• All norms on a finite dimensional vector space are equivalent. math.mit.edu/~stevenj/18.335/norm-equivalence.pdf – Elliot G 2 days ago
• So which norm would you use to show "each entry converges to the corresponding entry"? – Prasiortle 2 days ago
• @Prasiortle $\|A\|=\max \{|a_{ij}|: 1\leq i,j \leq n\}$ would be one such norm. – Kavi Rama Murthy 2 days ago
• Thanks very much! – Prasiortle 2 days ago