Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

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

Let $V=K^{n+1}$ be a vector space of dimension $n+1$ and $\mathbb{P}V$ the projective space associated to $V$. How to identify the homogeneous coordinates on $\mathbb{P}V$ with the elements of $V^*$? Thank you very much. I think that the homogeneous coordinates on $\mathbb{P}V$ are $Z_0, \ldots, Z_n$, where $Z_0, \ldots, Z_n$ are standard coordinates on $K^{n+1}$.

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

As you wrote, $Z_i$ is a standard coordinate on $K^{n+1}$, in other words a linear map $Z_i: K^{n+1}\to K$, in other words an element of $V^*$ where $V=K^{n+1}$.

share|cite|improve this answer

Precisely. And those are nothing but (the standard basis) elements of $V^*$.

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.