What is the correct way to multiply matrices?

[i.l]

Hey,

When trying to multiply the 2 attached matrixes (row X column) I get a much more terms then the attached answer.
C is for cos and s for sin.
What am I doing wrong?
Regards,
i.l

 

[elibj123]

You mean you don't have terms canceling out?

I suggest working carefully and invoking some trigonometric identities.

 

[Mark44]

I get it that c stands for cosine and s stands for sine, but what does c₁ mean? Cosine of what? Sine of what?

In one of your multiplications you have c₁ in one matrix and c₂ in the other, and you wrote the product as c₁₂. What does that mean?

 

[Simon_Tyler]

Simply typing it into Mathematica and using FullSimplify gets the results that you want. It is merely a combination of trig identities - namely the http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities".

The tricky bit is in the top 2*2 block - I suggest you look at the math for multiplying 2d rotation matrices.

$$A(\text{x\_})\text{:=}\left(<br /> \begin{array}{cccc}<br /> \cos (x) & -\sin (x) & 0 & a(x) \cos (x) \\<br /> \sin (x) & \cos (x) & 0 & a(x) \sin (x) \\<br /> 0 & 0 & 1 & 0 \\<br /> 0 & 0 & 0 & 1<br /> \end{array}<br /> \right)$$

$$A(x).A(y)=\left(<br /> \begin{array}{cccc}<br /> \cos (x+y) & -\sin (x+y) & 0 & a(x) \cos (x)+a(y) \cos (x+y) \\<br /> \sin (x+y) & \cos (x+y) & 0 & a(x) \sin (x)+a(y) \sin (x+y) \\<br /> 0 & 0 & 1 & 0 \\<br /> 0 & 0 & 0 & 1<br /> \end{array}<br /> \right)$$