Let Mn×n be the space of real n×n matrices, regarded as a metric space with the distance function
\(\displaystyle d(A,B)=\sum_{i,j} |a_{ij}-b_{ij}|\)
for A=(aij) and B=(bij).
Prove that \(\{A\in M_{n\times n}: A^m=0 \text{ for some positive integer }m\}\) is a closed set.
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2010-10 Metric space of matrices,
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