I was thinking about the following problem
$V$ is a vector space over a field $K$ and $E$ is a vector space over a field $F$. Is it possible to define a linear mapping from $V$ to $E$ ?
I was thinking about this because I wanted to show that a linear application verifies the following property:
$L(0_{V})=0_{E}$
but I was stuck since I didn't have more information about the fields considered on the starting and ending vector space.
Thank you a lot !