circularly symmetric gausian random variables

Dear friends i need a help in building a 4x4 matrix with elements being zero mean and unit variance independent and identically distributed (i.i.d.) circularly symmetric Gaussian variables.

i tried this but i m not sure is it correct or not

x=randn(1,4);

c= x+i.*x;

d= toeplitz(c);

[Image Analyst]

What does circularly symmetric mean, and why do you want it? Give an example.

Shouldn't x be randn(4,4)? What you calculated was a 1 by 4 row vector, not a 4 by 4 matrix. Why are you not done once you calculate x? I don't see how shuffling the values around gains you anything at all.

[Roger Stafford]

I too am not sure what you mean by "circularly symmetric". Would the following satisfy your definition? It involves just three independent random variables.

 A = randn(2);
 A(2,1) = A(1,2);
 A = [A,fliplr(A)];
 A = [A;flipud(A)];

[sadeq]

"Circular" means the variance of the real and imaginary parts are equal. Also the variables should be complex. Then, to satisfy this, I hope id this clear so I can get the right answer

I also tried to do the following

x= randn(4,4)
c= x+i.*x % i is the imaginary variable.

[Image Analyst]

So what's wrong with that? The real and imaginary parts must have the same variance because they were built with the same array (x).