Vector normalization: Difference between revisions

Revision as of 20:07, 6 February 2006

Revision as of 20:10, 6 February 2006

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Vector Normalization

Objective:

Transform a vector so that its norm (or length) is equal to 1.

Procedure:

Given an n-dimensional vector x, its normalized version r is calculated by:

ri = xi/squareroot(sum_j=1..n(xj^2)), for i = 1...n;

Example:

given the 3-dimensional vector x = (3, 4, 5), i.e. x1 = 3, x2 = 4 and x3 = 5, its normalized version will be:

r1 = 3 / squareroot(sum(3^2+4^2+5^2))

r1 = 0.424

r2 = 4 / squareroot(sum(3^2+4^2+5^2))

r2 = 0.566

r3 = 5 / squareroot(sum(3^2+4^2+5^2))

r3 = 0.707

r = (0.424, 0.566, 0.707)

to verify the answer, one can compute the resulting norm:

||r|| = (0.424^2 + 0.566^2 + 0.707^2) = 1.000;