how to span a 3*1 vector into a 3*3 skew symmetric matrix ?

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Hi everyone, as the title,
x=[a b c]' is a 3*1 vector, and its 3*3 skew symmetric matrix is
X=[0 -c b ;
c 0 -a ;
-b a 0 ];
what command is all right to make it in Matlab ?
THX very much!
Cheers
  2 Comments
Thanacha Choopojcharoen
Thanacha Choopojcharoen on 12 Oct 2023
Edited: Thanacha Choopojcharoen on 12 Oct 2023
I wrote a vectorized version of skew where v can be 3xn or nx3. This will return 3x3xn. Technically, this can be defined as a one-line anonymous function as well.
function S = skew(v)
a = size(v,1)==3;
n = size(v,round(1+a));
V = permute(v,[round(2-a),3,round(1+a)]);
I = repmat(eye(3),[1,1,n]);
S = cross(repmat(V,[1,3]),I);
end

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Accepted Answer

Sean de Wolski
Sean de Wolski on 18 Jun 2014
X=[0 -x(3) x(2) ; x(3) 0 -x(1) ; -x(2) x(1) 0 ];
  3 Comments
John D'Errico
John D'Errico on 19 Jun 2014
A great virtue of MATLAB (ok, almost any programming language) is the ability to write functions that do what you want. Making a skew-symmetric matrix from a vector is not something most people will ever need to do, so it is unlikely you would find a simple command to do it. However, since you can write functions that do anything you want, anything that you will do often, then do so. Personalize your version of MATLAB to include such tools that do what you have a need for.
In this case, a simple m-file would suffice. Or write a function handle if this is not something you will have a need for beyond today.
Finally, the code that Sean gives is easily vectorized to create a 3-d array, where each plane would be one such matrix.

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More Answers (3)

Sergei Sergienko
Sergei Sergienko on 5 Jun 2020
Edited: Sergei Sergienko on 5 Jun 2020
There is special function for this in Matlab called skew
v = [1 2 3]';
skew(v)
ans =
0 -3 2
3 0 -1
-2 1 0
  2 Comments
Mitsu
Mitsu on 3 Dec 2020
This function is not included, as of MATLAB 2019b; unless it is part of a specific additional toolbox.
Elyar Zavvari
Elyar Zavvari on 12 Aug 2021
You will find this function in matlab robotics toolbox by Kevin Lynch.

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Raul Cajias
Raul Cajias on 20 Apr 2016
I think what you're looking for is the skewdec skewed function. However it's only available with the 'Robust Control Toolbox'.

Wit
Wit on 15 Sep 2019
Edited: Wit on 15 Sep 2019
I think there is a "cross2Matrix" function:
x = [1; 2; 3];
cross2Matrix(x)
ans =
0 -3 2
3 0 -1
-2 1 0

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