How can we create two vectors have normally distributed random entries with zero mean?

How can we create two vectors have normally distributed random entries with zero mean , and they are scaled so that in Matlab.

Answer 1

[Bruno Luong]

I correct the flaw of dpb method

U=randn(10,1);
V=randn(10,1);
ps=U.'*V;
a=sqrt(abs(ps));
U=(sign(ps)/a)*U;
V=(1/a)*V;

[dpb]

Ah! Good catch, Bruno! Thanks.

Answer 2

[dpb]

>> uv=randn(1000,2);
>> uv=uv/sqrt(sum(uv(:,1).*uv(:,2)));
>> uv(:,1).'*uv(:,2)
ans =
    1.0000
>> mean(uv)
ans =
    0.0025    0.0091
>>  

[Omar B.]

Thank you for the response, but I want to construct two vectors U and V . They both have normally distributed random entries with zero mean, and also .

[dpb]

uv(:,1) and uv(:,2) are vectors with such properties...just created them as an array--name them however you wish.

[Bruno Luong]

the sqrt() might be imaginary (1/2 chance)

>> uv=randn(10,2); uv=uv/sqrt(sum(uv(:,1).*uv(:,2)))

uv =

   0.0000 + 0.3856i   0.0000 + 0.0703i
   0.0000 + 0.9468i   0.0000 - 1.0239i
   0.0000 + 0.0416i   0.0000 - 0.9650i
   0.0000 + 0.1552i   0.0000 + 0.0931i
   0.0000 - 0.1422i   0.0000 + 0.4418i
   0.0000 - 0.7345i   0.0000 + 1.1256i
   0.0000 - 0.4265i   0.0000 - 0.4973i
   0.0000 - 0.9666i   0.0000 - 0.0169i
   0.0000 + 0.5398i   0.0000 + 0.8718i
   0.0000 + 0.6400i   0.0000 + 0.2477i

[John D'Errico]

Normally distributed, with zero mean. You don't say if the sample mean should be zero, or the population mean zero. Normal samples from randn have a zero popiulation mean. But the sample mean just has an expected value of zero. A subtle difference that few people seem to appreciate when they lack the proper background.

Anyway, it is easy enough to scale them so the dot product is also 1. I could keep them as separate vectors, since that seems to have confused you, but you need to LEARN TO USE MATRICES.

uv = randn(1000,2);
dp = uv(:,1)' * uv(:,2);

uv = uv/sqrt(abs(dp));
if dp < 0
  uv(:,1) = -uv(:,1);
end

As you can see, the dot product is 1. Note that the code I gave you will not end up 50% of the time with an imaginary square root.

uv(:,1)'*uv(:,2)
ans =
                         1
                         
mean(uv)
ans =
      -0.00248985528111534      -0.00172138844051432

The sample means are not identically zero, but you were not specific there, and that is simply repaired.

Do you really think you need disrinctly named vectors? LEARN TO USE MATLAB! The mat in MATLAB stand for matrix.

u = uv(:,1);
v = uv(:,2);