Sign up ×
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.

Let $M$ be the set of $(n+1)\times(n+1)$ symmetric, idempotent matrices of trace 1. What is the inverse function of $f:\mathbb{R}P^n\rightarrow M$ defined by $[x_1,\ldots,x_{n+1}]\mapsto\left(\frac{x_ix_j}{\sum x_k^{2}}\right)$?

share|cite|improve this question

1 Answer 1

The inverse function you want maps each such matrix to its image (its column space, if you like), which is a $1$-dimensional subspace, that is, a point of the projective space.

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.