How to center vector to mean zero?

Hi everyone,

I would like to center a vector A = randn(50,1) to center, meaning that (1/N)*sum(a(i)) = 0 , where a is the centered vector A, i = 1, .. ,50 and n=50. Moreover, if I have a matrix B = randn(50,4) how could we standardize it, meaning that (1/n)*sum(x(i))=0 and (1/n)*sum(x^2)=1, namely they follow a normal distribution with zero mean and unit variance N(0,1). Could anyone help with these two problems?

[Rik]

You mean something like x=x-mean(x);? You notation isn't very clear, nor what it precisely is you want to do.

Answer 1

[John D'Errico]

Standardize a vector, by centering to have mean 0, and variance 1.

x = rand(100,1);
x = (x-mean(x))/std(x);

Subtracting the mean centers it. Dividing by the standard deviation is independent of the mean, but it sets the standard deviation (and thus the variance) to 1.

mean(x)
ans =
   7.6605e-17

std(x)
ans =
            1

var(x)
ans =
            1

The population parameters are as close to 0 and 1 as floating point computations can ensure.