cross product of by an array

I have (a )which is an array as below:

a =

a{1} = [185x3 double]

a{2} = [185x3 double]

a{3} = [185x3 double]

a{4} = [185x3 double]

a{5} = [185x3 double]

Also I have (L)which is (5,3) matrix

I need to make cross product as below

(0,0,-2) x a{1} = [185x3 double]

0,0,-1 x a{2} = [185x3 double]

0,0,0) x a{3} = [185x3 double]

0,0,1) x a{4} = [185x3 double]

0,0,2) x a{5} = [185x3 double]

this should result another vectors which I need to quiver3 them

thanks in advance

Answer 1

[Todd]

You can represent a cross product as a matrix product

a X b = tilde(a)*b

where tilde(a) is a skew-symmetric matrix defined by

tilde = @(v)[ 
    0      -v(3)    v(2)
    v(3)    0      -v(1)
    -v(2)    v(1)    0
    ];

For example

a = [0;0;-1];
b = [1;2;3];
c = tilde(a)*b

b could be a 3xm matrix of column vectors, in which case tilde(a)*b is a crossed with each column of b.

a = [0;0;-1];
b = rand(3,185);
c = tilde(a)*b

Also note that tilde(a)*b = -tilde(b)*a.

My example assumes column vectors, so you'll have to transpose things to apply it to your data.

[Oday Shahadh]

thanks Todd, sorry I made a mistake in typing my question

the range is from(0,0,-2) to (0,0,2) as seen above