(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let V be a vector space over a field K. Let S be a set of vectors of V,

S= {e_i : i in J} (i.e e_i in V for each i in J) where J is an index set.

Prove that if S satisfies the following property, then S must be a basis.

The property is:

For every vector space W over the field K and for every function f: S-> W there exists

a unique linear transformation T: V-> W such that T restricted to S = f.

3. The attempt at a solution

I really have no clue how to start this, of course I must prove its linearly independent

and its spans V.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Vector space proof

**Physics Forums | Science Articles, Homework Help, Discussion**