An isomorphism sends a basis to a basis: injectivity preserves independence and surjectivity gives spanning. Hence isomorphic spaces have the same dimension. Scalar fields must be fixed; $\mathbb C$ has dimension one over itself but dimension two over $\mathbb R$.
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.