Re: Is there a possibility to have more than one ZERO vector in a space!?
- From: "kunzmilan" <kunzmilan@xxxxxxxx>
- Date: 3 Nov 2006 04:03:37 -0800
The metric space (S, sigma). S is a set of
sequence of observations.
s1=[1, 2, 3, 3, 4, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9] belongs to S.
s2=[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] belongs to S too.
s1+s2=[2, 3, 4, 4, 5, 4, 4, 4, 4, 5, 6, 7, 8, 9, 10] also belongs to S.
sigma is the standard deviation of the observations.
Form a right triangle from the first two observations from s1. Find
their vector sum. To the end of the sum, add the third vector in the
right angle. Either as the perpendicular to the plane of the first two
vectors or directly in the plane of the first two vectors. (A rotation
does not change the length of a vector.) Find again the sum.
At each step, its hypothenuse is the diameter of a circle in which the
right triangle can be filled in. One its leg is formed by the standard
deviation, the other is square root from n*(mean)^2. This procedure can
be made with any combination of sx. Different sequences of observations
can be compared.
But the zero vector is only one (0,0...0).
kunzmilan
.
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