Is var command works also for complex numbers?

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);

Answer 1

[Alex Mcaulley]

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    

[guy lasri]

Thanks for the fast answer. How is the variance different? And which variance is better for MMSE estimation?

[Steven Lord]

See the second and third paragraphs in the following section of the Wikipedia article on variance.