# Linear Functional "So, even though the interpretation of the objects (vectors vs. functionals) differs, the underlying structure of both spaces is identical" - given that the underlying structure is identical, is it fair to say that the interpretation of the objects comes from the semantics that we give it? "This geometric relationship highlights the connection between vectors and functionals: one describes direction, and the other measures projections along that direction." - can you say more about this and give a concrete example? TODO: Take this chatgpt thread and place it in here: [ChatGPT](https://chatgpt.com/share/e/671b0714-7078-8006-9db5-5840f73f0d8d) --- Date: 20241024 Links to: Tags: References: * []()