2-D Meshgrid Rotation Matrix Multiplication

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Sordin on 2 Apr 2017
Commented: Walter Roberson on 3 Apr 2017
I am trying to rotate the coordinates of a 182x182 mesh grid by means of multiplication with the rotation matrix: The following code works fine:
[x0,y0] = meshgrid(x,x);
for i = 1:length(theta)
X = x0.*cosd(-i) + -y0.*sind(-i);
Y = x0.*sind(-i) + y0.*cosd(-i);
end
However, I get errors when I try to perform this using the following matrix multiplication: Here is my code:
[x0,y0] = meshgrid(x,x);
for i = 1:length(theta)
R = [cosd(-i) -sind(-i); sind(-i) cosd(-i)];
[X,Y]'=R.*[x0;y0];
end
And this is the error:
[X,Y]=R.*[x0;y0];
The expression to the left of the equals sign is not a valid target for an assignment.
And when I remove the transpose operator, it says:
Error using .*
Too many output arguments.
What is wrong here? How can I perform this operation using matrix multiplication?
Any guidance is greatly appreciated.

Stephen on 2 Apr 2017
Edited: Stephen on 2 Apr 2017
Firstly you are using the wrong multiplication operator: you need to use matrix times *, not element-wise times .*.
Secondly you are trying to implicitly split the output of this multiplication into parts. But the output of that multiplication is one column vector. Therefore you need to allocate the output to one variable:
Z = R*[x0;y0]
When you write [X,Y] = ... then you are telling MATLAB that the operation has two output variables. But a multiplication does not have two outputs, it only has one.
You have other bugs in your code as well, such as using i as the input to sin and cos, whereas you should use theta(i).
Walter Roberson on 3 Apr 2017
XY = R * [x0(:), y0(:)] .';

Walter Roberson on 2 Apr 2017
You have
[X,Y]'=R.*[x0;y0];
You need to replace this with something like
XY = R * [x0;y0];
X = XY(1);
Y = XY(2);
Sordin on 3 Apr 2017
I'm very confused because R is definitely a 2x2 matrix:
R = [cosd(-i) -sind(-i); sind(-i) cosd(-i)]
For instance, for θ=1, the output is:
R =
0.9998 0.0175
-0.0175 0.9998
And x0 and y0 should be scalars because they are defined as:
n = size(Image,1);
x = linspace(-1,1,n);
[x0,y0] = meshgrid(x,x)
Why is it that this method doesn't work but the following non-matrix approach does?
X = x0.*cosd(-i) + -y0.*sind(-i);
Y = x0.*sind(-i) + y0.*cosd(-i);
Thank you.