A change-of-coordinates matrix is invertible because coordinate conversion is bijective. Its inverse changes coordinates back: $P_{C\leftarrow B}^{-1}=P_{B\leftarrow C}$. Converting $B$ to $C$ and back gives the identity, proving both inverse identities.
Parents
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.