# Change of Basis and Linear Transformations If you have an **invertible** linear transformation: $T: V \to V$ then there’s always an equivalent way to see it as: 1. **Active view** – transform the vectors themselves via $T$ while the basis stays fixed. 2. **Passive view** – change the basis via $T^{-1}$ while the geometric vectors stay fixed, so their _coordinates_ change in the opposite way.  Mathematically it does not matter if you take the active or passive view. They are just two ways of describing the same thing. You should pick the view that jives with your intuition in your problem context. --- Date: 20250812 Links to: Tags: References: * []()