This video goes into a lot more detail on the definition of the partial trace to calculate the reduced density matrix in a composite system.
This is part of the following series of videos on the Density Matrix and Mixed States: playlist: https://youtube.com/playlist?list=PLhI5X1mNN8ghnH1ckAcclxY6-CPmZvWrk
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References:
https://en.wikipedia.org/wiki/Partial_trace
