Question

Find a basis for the space V of all skew-symmetric 3x3 matrices. What is the dimension of V?

Answer 1

I'll be back in a sec. Brewing some coffee. Would you like some?

Answer 2

Yeah, I will in maybe two hours =P

Answer 3

Well you need to remember that a basis for any vectorial space generates it and it's vectors are linear independent.

Answer 4

And 3x3 skew-symmetric matrix is something like this:

Answer 5

\[A=-A^T\]

Answer 6

:-)

Answer 7

Hmm thinking...

Answer 8

Do you have any idea to begin with?

Answer 9

Mm you need three matrices am I right?

Answer 10

Well the dimension is 3 haha

Answer 11

I am stupid haha

Answer 12

and I need a longer explanation b/c A=-A^T isn't gonna cut it

Answer 13

soy estupido haha

Answer 14

uff
I almost burn my brain hehe

Answer 15

I told you linear algebra's no good!

Answer 16

Well I think that the three vectors are \[\left[\begin{matrix}0 & 1 & 0\\ -1 & 0 & 0\\ 0 & 0 & 0\end{matrix}\right]\]

Answer 17

Hmmm you're right

Answer 18

Is the idea of a basis clear to you?

Answer 19

Like you know why (1,0,0), (0,1,0),(0,0,1) is the basis of R^3?

Answer 20

yes.

Answer 21

Well then you know that the basic idea behind a basis is that you can get any vector of the space by forming a linear combination.

Answer 22

like \[\vec{v}=a\hat{i} + b\hat{j} + c\hat{k}\]