Assume that V is finite-dimensional and S, T ∈ L (V). Show that dim ker(ST) ≤ dim ker(S) + dim ker(T).
I am confused to what L(V) is defined as here because L should be linear transformations from V to some other space W.
But I think L(V) should be defined HERE AS linear transformations from/to V to/from some other space W such that S ∈ L(V, W), T ∈ L(U, V ). Am I correct in assuming this or should S ∈ L(V, W), T ∈ L(V, U )? (but then the composition makes no sense?)