skewVee.m

function x = skewVee(X)

    % SKEWVEE generates a [3 * 1] vector from a [3 * 3] matrix. In particular,
    %         this function does two operations: first, it creates the skew 
    %         symmetric matrix of the form (X - X')/2, and then retrives from 
    %         this skew symmetric matrix the [3 * 1] vector composing it.
    %
    % FORMAT: x = skewVee(X)  
    %
    % INPUT:  - X = [3 * 3] matrix
    %
    % OUTPUT: - x = [3 * 1] vector 
    %
    % Authors: Daniele Pucci, Marie Charbonneau, Gabriele Nava
    %          
    %          all authors are with the Italian Istitute of Technology (IIT)
    %          email: name.surname@iit.it
    %
    % Genoa, Dec 2017
    %

    %% --- Initialization ---

    % skew symmetric part of X
    X_skew  = 0.5*(X - transpose(X)); 
    
    % vector composing the matrix
    x = [-X_skew(2,3)
          X_skew(1,3)
         -X_skew(1,2)];
end