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How to center vector to mean zero?

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gsourop
gsourop 2017-11-9
回答： John D'Errico 2017-11-9
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?
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Rik
Rik 2017-11-9
You mean something like x=x-mean(x);? You notation isn't very clear, nor what it precisely is you want to do.

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John D'Errico
John D'Errico 2017-11-9
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.

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