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 tried to find a basis for the subspace of 3-by-3 anti-symmetric matrices - but for nothing.

How to find such a basis?

share|improve this question
    
I take it you mean the basis of the vector space of all antisymmetric $3 \times 3$ matrices? (A matrix doesn't have a basis.) –  Clive Newstead Jan 7 '13 at 11:10
    
@CliveNewstead of-course it doesn’t that’s why I mentioned the fact the I need to find the sub-space of the Matrix... –  Billie Jan 7 '13 at 11:17
    
A matrix doesn't have subspaces either! –  Clive Newstead Jan 7 '13 at 11:19
    
I've edited your question. If it doesn't reflect what you mean precisely, please feel free to roll back. –  user1551 Jan 7 '13 at 12:04
    
In addition to being a subspace, it is also a Lie algebra denoted by $so(3, \mathbb{R})$. –  PAD Jan 7 '13 at 12:43
show 1 more comment

1 Answer

up vote 2 down vote accepted

Hint 1: What value must the diagonal entries take? And if the value of the $(i,j)^{\text{th}}$ entry is $a$, what is the value of the $(j,i)^{\text{th}}$ entry?

Hint 2: Hover over the grey box below when you've thought a bit about Hint 1.

The bottom-left entries are determined by the upper-right entries, over which you have free choice.

share|improve this answer
    
Maybe I kinda forgot to mention, "Find the Basis and the dimension of an Anti Symmetric sub-Space arrangement 3x3" –  Billie Jan 7 '13 at 11:15
    
@user1798362: I don't understand what you mean. I presume you're trying to find a basis for the subspace (of the $9$-dimensional vector space of all $3 \times 3$ matrices) consisting of the antisymmetric matrices. –  Clive Newstead Jan 7 '13 at 11:21
    
yes.............. –  Billie Jan 7 '13 at 11:24
2  
Ok $-$ well that's what my hints are working towards. If you need another hint, let me know! –  Clive Newstead Jan 7 '13 at 11:28
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.