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 2 years ago
Find a basis for the space V of all skewsymmetric 3x3 matrices. What is the dimension of V?
 2 years ago
Find a basis for the space V of all skewsymmetric 3x3 matrices. What is the dimension of V?

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brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0I'll be back in a sec. Brewing some coffee. Would you like some?

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Yeah, I will in maybe two hours =P

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Well you need to remember that a basis for any vectorial space generates it and it's vectors are linear independent.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2And 3x3 skewsymmetric matrix is something like this:

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Do you have any idea to begin with?

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Mm you need three matrices am I right?

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Well the dimension is 3 haha

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0and I need a longer explanation b/c A=A^T isn't gonna cut it

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2uff I almost burn my brain hehe

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0I told you linear algebra's no good!

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Well I think that the three vectors are \[\left[\begin{matrix}0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 0\end{matrix}\right]\]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Is the idea of a basis clear to you?

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Like you know why (1,0,0), (0,1,0),(0,0,1) is the basis of R^3?

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Well 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.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2like \[\vec{v}=a\hat{i} + b\hat{j} + c\hat{k}\]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2well that is the idea in a graphic form.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2If you want to obtain a basis for the 3x3 skew symmet

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2ric matrices you need to know that is the general form of matrix of that kind.

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0okay, I'm following what you're saying

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2the definition says that the elements of an skew symmetric matrix are such as: \[a_{ij}=a_{ji}\]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2It seems that that doesn't tell us a lot about those matrices, but you can figure out what you have on the diagonal.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2if i = j, then \[a_{ii}=a_{ji}\]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2which is true if the diagonal is made up zeros.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2and I think that's all. An 3x3 skew symmetrical matrix has this form:

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0Here's something... http://www.euclideanspace.com/maths/algebra/matrix/functions/skew/index.htm

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2\[\left[\begin{matrix}0 & a_{12} & a_{13} \\ a_{12} & 0 & a_{23}\\ a_{13} & a_{23} & a_{33} \end{matrix}\right]\]

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0Looks like it's all zeros down the diagonal.

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0you're a bad math teacher haha! :p

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2well now you can split that matrix on three parts:

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0Yep this part is where I need explaining...

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2\left[\begin{matrix}0 & a_{12} & 0 & \\ a_{12} & 0 & 0\\ 0&0&0\end{matrix}\right]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2\[\left[\begin{matrix}0 & 0 & a_{13} & \\ 0 & 0 & 0\\ a_{13}&0&0\end{matrix}\right]\]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2\[\left[\begin{matrix}0 & 0 & 0 & \\ 0 & 0 & a_{23}\\ 0&a_{23}&0\end{matrix}\right]\]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Is it clear why I did that?

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0Oh I see. So each part of the basis will be a 3x3 matrix?

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0And there will be (3) 3x3 matrices

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2yeah! it has to bee a 3x3 matrix

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0I asked on cramster and some (puta) was really insulting to me AND she gave me the wrong answer.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2what is cramster? and puta?

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2we are not finished yet.

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0I thought it meant b)it(ch but I guess it's mexican slang for prostitute or whore

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0but you get the idea.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2\[\left[\begin{matrix}0& 1 & 0 \\ 1 & 0 &0\\ 0&0&0\end{matrix}\right]\]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2ahh I thought I did haha.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2\[\left[\begin{matrix}0& 0 & 1 \\ 0 & 0 &0\\ 1&0&0\end{matrix}\right]\]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2and \left[\begin{matrix}0& 0 & 0 \\ 0 & 0 &1\\ 0&1&0\end{matrix}\right]

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2You multiply by the scalars a,b,c each of those matrices and form a linear combination.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2and the result is a skew symmetrical matrix

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2I'm sorry If my explanation was awful, and my english worst =P

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0So the dimension of all skewsymmetric matrices is 2?

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0or that's only the dimension of the basis?

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2the dimesion is the number of vectors of the basis. so it's 3.

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0hahaha I am so stupid!

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0WOW. I can't believe I asked that.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2if you have an 4x4 skew symmetrical matrix the dimension of the basis is 4.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Don't worry, don't judge yourself so severely.

Nodata
 2 years ago
Best ResponseYou've already chosen the best response.2Do you have any doubt regarding this brinethery?

brinethery
 2 years ago
Best ResponseYou've already chosen the best response.0I have another question for you! No I don't have any doubt. You did a great job explaining.
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