Probability vector: Difference between revisions

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===Some Properties of <math>n</math> dimensional Probability Vectors===

: Probability vectors of dimension <math>n</math> are contained within an <math>n</math> dimensional unit [[hypersphere]].

: The shortest probability vector has the value <math> 1/n </math> as each component of the vector, and has a length of <math>1/\sqrt n</math>.

: The longest probability vector has the value 1 in a single component and 0 in all others, and has a length of 1.

: The shortest vector corresponds to maximum uncertainty, the longest to maximum certainty.

: No two probability vectors in the <math>n</math> dimensional unit hypersphere are collinear unless they are identical.

: Given that every possible state of a system under consideration is assigned to one and only one component of the vector, then the probability value of each component may be expressed as a rational number with <math>n</math> as the common denominator.

==See also==