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 am working on example of vector space. I have question:

Let $\{V_1,V_2,\ldots,V_t\}$ be a family of $n$-dimensional subspaces and the dimension intersection of any $n$ subspace is at least one. Is it true

$\dim \bigcap^{i=t}_{i=1}V_i\geq1$?

I have calculated $\dim \bigcap^{i=t}_{i=1}V_i$ for several spaces and all of spaces satisfied in $\dim \bigcap^{i=t}_{i=1}V_i\geq1$.

Can any body take counter example? Thanks.

share|improve this question
    
Each $V_i$ is $n$-dimensional. But you are taking exactly $n$ to take intersections? –  Sigur Jun 30 '12 at 21:03
    
@Sigur yes exactly –  Babak Miraftab Jun 30 '12 at 21:06
    
After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark ✓ next to it. This scores points for you and for the person who answered your question. If you don't do this, people are less likely to answer your later questions. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?, How does accept rate work?. –  Michael Albanese Dec 31 '12 at 15:08
add comment

1 Answer 1

Consider the vector space $\mathbb{R}^3$. Let $t = 3$ and $n = 2$. Consider $V_1$ to be the $xy$ plane. $V_2$ to be the $xz$ plane. $V_3$ to be the $yz$ plane. All of these are $2$ dimensional subspaces. The intersection of any pair is one dimensional line. However the intersection of all three is just the origin which is not $1$-dimensional.

share|improve this answer
    
ok thanks,it is very helpful –  Babak Miraftab Jun 30 '12 at 21:07
add comment

Your Answer

 
discard

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.