Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a large linear inequality system of the form $Ax ≤ 0$.
Is there a way to solve this system using linear algebra tools like SVD?

share|cite|improve this question
up vote 1 down vote accepted

No; loosely speaking this problem is more related to linear programming, which is not equal to linear algebra.

(Plugging in an SVD of $A$ will be too helpful as you probably have seen.)

The set $Ax\leq 0$ is a convex polytope and the representation $Ax\leq 0$ is called its H-representation because it is a description as intersection of half-spaces. Another representation is its V-representation which consists of a list of the vertices. The Wikipedia entry on convex polytopes has more pointers.

share|cite|improve this answer
Yes, that's what I thought. I know it can be solve using linear-programming, and indeed, my desired solution is the list of vertices. Thanks. – Adi Shavit Jul 24 '12 at 5:53

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.