MathOverflow is a question and answer site for professional mathematicians. 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

Given three sets of vectors $S_i=\left(V_{i1},V_{i2},\ldots,V_{in}\right),i=1,2,3$, s.t. the vectors within a set are pair-wise orthogonal and $V_{ij}\cdot V_{kl}\geq 0$ $\forall i,j,k,l$. Also, $\sum_jV_{ij}=w$ $\forall i$ where $w$ is some unit vector and $V_{ij}\cdot w=V_{ij}\cdot V_{ij}$ $\forall i,j$. It is given that the vectors in $S_i,S_j$ $\forall i\neq j$ lie in $R_{\geq 0}^k$ for some $k$. Can all the three sets of vectors be accommodated in $R_{\geq 0}^K$ for some $K$?

share|cite|improve this question
isn't this similar (but not same as) to what people used to try to do to a PCA solution to rotate it to become sparse? – Suvrit Jun 27 '11 at 14:23

Your Answer


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

Browse other questions tagged or ask your own question.