How can you "rigorously" prove the following mathematical fact? $$ \sum_{k=0}^m \sum_{j=0}^k a_{kj} = \sum_{j=0}^m \sum_{k=j}^m a_{kj} $$
Visually, it is clear they are equivalent (https://math.stackexchange.com/a/1395905/635480)
2026-04-30 00:08:41.1777507721
Double Summation Indices Switching
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