# Guidance: Convex hull, null space and convex basis etc

1. Feb 20, 2014

### Inner_Peace

Hi friends!
I am getting started with a research paper that discusses the closure properties of a robotic grasp. There are of lot of mathematical terms that confuse me like 'convex hull' , convex basis, convex combination of vectors, a free subset, nullspace etc. I might have studied some of them in University mathematics but that seems a long ago. Could you please suggest me places where should I start looking for concept building ? Any good tutorials or books?

Thank you ! :)

2. Feb 21, 2014

### mathman

Have you tried to google these terms?

3. Feb 22, 2014

### HallsofIvy

I don't see this as having much to do with vectors. A "convex set" in $R^n$ is a set such that for any two points p and q in the set the line segment between p and q is in the set also.

The "convex hull" of a set, A, is the smallest convex set that has A as a subset. One way to construct the convex hull of a set is to add all line segments between any two points in the set.

I don't recognize the terms "convex basis", "convex combination", or "free space".

The "null space" of a linear Transformation, T, from one vector space to another, is the set of all vectors, v, such that T(v)= 0. One can show that the null space is a subspace of the domain vector space.

4. Feb 23, 2014

### FactChecker

Amazon.com has several books on the subject. You will need to look at the reviews to see what fits your needs.
A convex basis is a set of vectors that can be added together with positive weights (all weights 0<=w<=1 that sum to 1). Those weighted sums are the convex combinations.