Proving Existence of Linear Mapping with Kernel in Subspace S | Helpful Guide

Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
1 reply · 2K views
Bazzinga
Messages
45
Reaction score
0
Hey guys, I was wondering if you could help me out with a question I've got, I really don't know where to go or really where to start! Here's the question:

Let S be a subspace of a finite dimensional vector space V. Show that there exists a Linear Mapping L: V → V such that the kernel of L is S.

I started off messing around with some examples and the theorem makes sense to me, I just can't figure out how to prove it! If someone could start me off that would be awesome.

Thanks!
 
Physics news on Phys.org
Take the orthogonal projection to the complement subspace of S.