Why does this matrix multiplication work?

Hi,

I had a look at the Simmechanics Demo mech_bouncing_ball.mdl because I want to find out how to model ground.

In the subsystem that calculates the force that acts on the ball when hitting the floor is a matrix multiplication.

It is calculated with a Gain-Block. The input is a 1x3 Matrix, the Gain Parameter is [0 0 0;0 0 0;0 0 -ball.pengain] and the output is again a 1x3 matrix. The Setting of the calculation is "Matrix(K*u)". The Help says: "The input and gain are matrix multiplied with the input as the second operand."

I dont't understand how this works. How is it possible that a 3x3 matrix is multiplied with a 1x3 matrix? When I try that in the comand window it says that "Inner matrix dimensions must agree." Why does it work with the Gain Block?

Would be great if someone could help me. I really don't understand that. Thank you very much!

Answer 1

[David Sanchez]

What's wrong with it?

a=rand(1,3);
b=rand(3,3);
c=a*b;

[Andrew Reibold]

I believe the question lies in the part where it says specifically that the input is the second operand which would make it

a=rand(1,3);
b=rand(3,3);
c=b*a;

[Iain]

Its using the vector, as a column. eg

 A = [0 1 0; 1 0 0; 0 0 1];
 B = [2 3 4];
 C = A*B';
 C = [3; 2; 4]

[Philipp]

Exactly Andrew, thats what I meant. @lain: But the output of the gain block is not a 3x1 Matrix but again 1x3. I guess it transforms it back after the multiplication. But why does that happen? And in which cases does it do that?

I don't find that very logical..