For an ordered basis $B=(b_1,\ldots,b_n)$ of $\mathbb F^n$, set $P_B=[b_1\ \cdots\ b_n]$. It converts basis coordinates to standard coordinates: $x=P_B[x]_B$. The reverse conversion is $[x]_B=P_B^{-1}x$. State the direction explicitly; both matrices are sometimes called change-of-coordinates matrices.
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.