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I'm just starting to realize that there are whole other levels of depth of understanding underneath this geometric intuition. So if you manage to grasp what is in these videos, don't stop! It keeps getting deeper and more mysterious, [1][2].

[1] https://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem#R...

[2] http://math.ucr.edu/home/baez/week233.html




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