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

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Omar B.
Omar B. on 8 Sep 2019
Edited: Omar B. on 12 Sep 2019
How can we create two vectors have normally distributed random entries with zero mean , and they are scaled so that in Matlab.

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dpb
dpb on 8 Sep 2019
>> 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
>>

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dpb
dpb on 8 Sep 2019
uv(:,1) and uv(:,2) are vectors with such properties...just created them as an array--name them however you wish.
Bruno Luong
Bruno Luong on 8 Sep 2019
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
John D'Errico on 8 Sep 2019
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);

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