Linear Algebra MT23, Homomorphisms
Flashcards
What is the vector space $\mathrm{Hom}(V, W)$?
The vector space formed by all linear maps between $V$ and $W$.
How can you see that if $\dim V = n$ and $\dim W = m$, then $\dim \mathrm{Hom}(V, W)$ will be $nm$?
Consider the matrices representing the linear transformations.