# What is a basis for the space of anti-symmetric $3\times 3$ matrices?

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?

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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

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?
@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
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