"Error using *". Help with my Monte Carlo Simulation

I have created code on low rank assumption using nuclear norm using CVX. I'm thinking this error code is being caused by the variable X not being recognised but im not sure. Here is the following error code -

Error using *

Incorrect dimensions for matrix multiplication. Check that the

number of columns in the first matrix matches the number of rows

in the second matrix. To perform elementwise multiplication, use

'.*'.

Error in Untitled34 (line 36)

y(i_p) = trace(M_p{i_p}*X);

Related documentation

Here is my code :

clear all; 
clc; 

MONTE_CARLO = 10;
n = 10;
m = 20;
k = 5;
U = randn(m,k);
V = randn(k,n);
X = U*V

for p = 1 : 50  : n^2          % Number of measurements    
    for mc = 1 : MONTE_CARLO   % Monte Carlo simulations        
        M_p = cell(p, 1);      % Cell with measurement matrices        
        y = zeros(p, 1);       % Vector of measurements        
        for i_p = 1 : p        % Generate measurement matrices            
            M_p{i_p} = randn(n, n);            
            y(i_p) = trace(M_p{i_p}*X);            
        end
        cvx_begin        
        variable Xe(n,n);        
        minimize(norm_nuc(Xe));        
        subject to
        
        for i_p = 1 : p            
            trace(Xe*M_p{i_p}) == y(i_p);
        end
        cvx_end
    end
end

[Jan]

Do you see, that your code is hard to read? Please format it as code and remove the pile of blank lines.

[Karim Wahdan]

@ Ok I have removed most of the blank lines it should be better now

[Bob Thompson]

'Please format it as code'

Jan is referring to the option to 'Insert a line of code' in the posting section. You can also select the block of code and press Alt+Enter.

It looks like X is defined to be a 20 x 10 size matrix, but M_p{i_p} is defined as a 10 x 10 matrix. You can multiply X*M_p{i_p}, but not the other way around.

Perhaps you want the transpose of X?

[Karim Wahdan]

@Bob Thompson By using X*M_p{i_p} instead of M_p{i_p} will cause the matrix not to be squared and the matrix has to be sqaured.

This means I will have to change the value of X or transpose it.

but how would I transpose X

[Bob Thompson]

Transposing a matrix is simple, just add an apostrophe after it.

X_Transpose = X';

You can also just include this in a greater equation

y(i_p) = trace(M_p{i_p}*X');

[Bob Thompson]

Now that I think about it, transposing X isn't going to give you a square matrix anyway. X is not a square matrix, but M_p{i_p} is, so no matter how you multiply them together they will not result in a square matrix output.

[Karim Wahdan]

@Bob Thompson What would you recommend then to fix this issue?

[Bob Thompson]

I don't know, because I don't know your problem statement to understand what X is supposed to be, or why you need a square matrix. It seems to me that this is not a MATLAB specific issue, and I recommend taking another look at the purpose for your code, rather than the specifics of the code itself. Sorry I can't be more help.