Take the 2-minute tour ×
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.

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|improve this question
1  
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

 
discard

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

Browse other questions tagged or ask your own question.