In textbook related to matrix analysis, when the concept of convergence of matrix is dealt, they give the topology using a norm. Since every norm is equivalent for finite dimensional vector space, we have only to pick a norm and observe the analytic things. However, there must exist a topology such that convergence situation which happens in above topology from a norm does not occur. My question is 'why do the books related to matrix analysis only consider topology from a norm when they discuss the concept of convergence?'.
2026-04-24 00:55:10.1776992110
Convergence of matrix and norm equivalence
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