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

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

[Sachin Goyal]

X = cross([x x x],eye(3))

[Thanacha Choopojcharoen]

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

Answer 1

[Sean de Wolski]

X=[0 -x(3) x(2) ; x(3) 0 -x(1) ; -x(2) x(1) 0 ];

[Stanley Cheng]

Hi Sean,

yeah you are right, but I mean if some command available directly to make it ? So we do not need to write so much, for I have several vectors to span into skew symmetric matrices.

[James Tursa]

Take Sean's code and make a function out of it.

[John D'Errico]

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.

Answer 2

[Sergei Sergienko]

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

[Mitsu]

This function is not included, as of MATLAB 2019b; unless it is part of a specific additional toolbox.

[Elyar Zavvari]

You will find this function in matlab robotics toolbox by Kevin Lynch.

Answer 3

[Raul Cajias]

I think what you're looking for is the skewdec skewed function. However it's only available with the 'Robust Control Toolbox'.

Answer 4

[Wit]

I think there is a "cross2Matrix" function:

x = [1; 2; 3];
cross2Matrix(x)
ans =
     0    -3     2
     3     0    -1
    -2     1     0