- In John Nash's class shown in A Beautiful Mind (5/11) Movie CLIP - Alicia's Solution (2001), what precisely is the problem and what exactly is the solution?
It looks to me that the $V$ is the solution of vector space $\mathbf{R}^3$ with vector field $F$ such that the $$ d \vec F =0,$$ while the $W$ is the solution of vector space $\mathbf{R}^3$ with vector field $F$ such that the $$ \vec F =d g.$$
Then the $ V/W $ is the quotient (kernel mod image) of the set such that $d \vec F =0,$ but $\vec F \neq d g$.
Then the $$ \dim(V/W) =? $$
- In Alicia's solution presented here, it was said that she assumed the vector field is a rational function $$ \vec F \in \mathbf{Q}.$$ What is her solution? Why incorrect? and what will be the correction to her solution?
(p.s. John Nash said: "Your solution is elegant, but on this particular occasion, ultimately incorrect.")
