MATLAB: Is var command works also for complex numbers

matlab functionvariance

Hey,
I tried to calculate variance on a complex matrix using the built in function 'var' and compared the results to the equetion 'Var = mean(abs(x).^2)-(abs(mean(x)).^2)'.
https://en.wikipedia.org/wiki/Complex_random_variable
I got different results. Any body know why?
This is the code:
x = [1, -1, 1+1i, 1-1i];
Var1 = var(x);
Var2 = mean(abs(x).^2)-(abs(mean(x)).^2);

Best Answer

If you take a look at the var documentation https://es.mathworks.com/help/matlab/ref/var.html you can see that the definition is not the same than the one you are using:
x = [1, -1, 1+1i, 1-1i];
Var1 = var(x)
Var2 = sum(abs(x-mean(x)).^2)/(numel(x)-1) %Following the definition
Var1 =
    1.6667
Var2 =
    1.6667
To use your definition of the variance, you have to put:
Var1 =  var(x,1)
Var2 =  mean(abs(x).^2)-(abs(mean(x)).^2)
Var1 =
    1.2500
Var2 =
    1.2500
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