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've been trying to read about partial fraction expansion of rational function.

Is the following statement equivalent to the uniqueness+existence of partial function expansion?:

Let $\mathbb{F}$ be an algebraically closed field and let $D=\{\frac{p}{q}~:~p,q\in\mathbb{F}[x],~\deg(p)\leq\deg(q)\}$. Consider $D$ as a linear space above $\mathbb{F}$. Then the set $\{(x-a)^{n}~:~a\in\mathbb{F},~n\leq0\}$ is a basis for $D$.

share|cite|improve this question
Yes. ${}{}{}{}$ – Qiaochu Yuan Jul 5 '12 at 14:14
We tend to say "as a vector space over $\mathbb F$" rather than "as a linear space above $\mathbb F$." But yes, this is correct. – Thomas Andrews Jul 5 '12 at 14:45

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.