The matrix of an inverse is the inverse of the matrix representation

Created almost 9 years ago, updated about 8 hours ago

If $T:V\to W$ is an isomorphism and $A=[T]_{C\leftarrow B}$, then $[T^{-1}]_{B\leftarrow C}=A^{-1}$. Composing the maps gives identity matrices in the relevant coordinates. The input/output bases reverse along with the map.

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.