Linear form

These notes are part of my notes on linear algebra.  I believe that textbooks of linear algebra give a bad definition of linear form.  The last section of the notes explain why it is bad.  I also give examples of linear form everyday life and from physics.  Given the vector space of distance, both force and electric field are dual spaces of the space of distance.  They are distict dual spaces of the space of distance, and they are not dual spaces to each other.  Also see a long thread of discussion titled "scalar done wrong"