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

Basic question about convexity/concavity:

Is the difference of a concave quadratic function of a matrix $X$ given by f(X) and a linear function l(X), a concave function?

i.e, is f(X)-l(X) concave?

If so/not what are the required conditions to be checked for?

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

A linear function is both concave and convex (here $-l$ is concave), and the sum of two concave functions is concave.

share|cite|improve this answer

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.