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- Maxwells_theorem abstract "In probability theory, Maxwell's theorem, named in honor of James Clerk Maxwell, states that if the probability distribution of a vector-valued random variable X = ( X1, ..., Xn )T is the same as the distribution of GX for every n×n orthogonal matrix G and the components are independent, then the components X1, ..., Xn are normally distributed with expected value 0, all have the same variance, and all are independent. This theorem is one of many characterizations of the normal distribution.Since a multiplication by an orthogonal matrix is a rotation, the theorem says that if the probability distribution of a random vector is unchanged by rotations and if the components are independent, then the components are identically distributed and normally distributed. In other words, the only rotationally invariant probability distributions on Rn that have independent components are multivariate normal distributions with expected value 0 and variance σ2In, (where In = the n×n identity matrix), for some positive number σ2.".
- Maxwells_theorem wikiPageID "309246".
- Maxwells_theorem wikiPageLength "1951".
- Maxwells_theorem wikiPageOutDegree "17".
- Maxwells_theorem wikiPageRevisionID "639872759".
- Maxwells_theorem wikiPageWikiLink Category:James_Clerk_Maxwell.
- Maxwells_theorem wikiPageWikiLink Category:Probability_theorems.
- Maxwells_theorem wikiPageWikiLink Characterization_(mathematics).
- Maxwells_theorem wikiPageWikiLink Expected_value.
- Maxwells_theorem wikiPageWikiLink Independence_(probability_theory).
- Maxwells_theorem wikiPageWikiLink James_Clerk_Maxwell.
- Maxwells_theorem wikiPageWikiLink Multivariate_normal_distribution.
- Maxwells_theorem wikiPageWikiLink Normal_distribution.
- Maxwells_theorem wikiPageWikiLink Orthogonal_matrix.
- Maxwells_theorem wikiPageWikiLink Philosophical_Magazine.
- Maxwells_theorem wikiPageWikiLink Probability_distribution.
- Maxwells_theorem wikiPageWikiLink Probability_theory.
- Maxwells_theorem wikiPageWikiLink Random_variable.
- Maxwells_theorem wikiPageWikiLink Statistical_independence.
- Maxwells_theorem wikiPageWikiLink Variance.
- Maxwells_theorem wikiPageWikiLink Vector_space.
- Maxwells_theorem wikiPageWikiLinkText "Maxwell's theorem".
- Maxwells_theorem hasPhotoCollection Maxwells_theorem.
- Maxwells_theorem wikiPageUsesTemplate Template:Cite_book.
- Maxwells_theorem wikiPageUsesTemplate Template:Cite_journal.
- Maxwells_theorem subject Category:James_Clerk_Maxwell.
- Maxwells_theorem subject Category:Probability_theorems.
- Maxwells_theorem comment "In probability theory, Maxwell's theorem, named in honor of James Clerk Maxwell, states that if the probability distribution of a vector-valued random variable X = ( X1, ..., Xn )T is the same as the distribution of GX for every n×n orthogonal matrix G and the components are independent, then the components X1, ..., Xn are normally distributed with expected value 0, all have the same variance, and all are independent.".
- Maxwells_theorem label "Maxwell's theorem".
- Maxwells_theorem sameAs m.01sz1m.
- Maxwells_theorem sameAs Q6796056.
- Maxwells_theorem sameAs Q6796056.
- Maxwells_theorem wasDerivedFrom Maxwells_theoremoldid=639872759.
- Maxwells_theorem isPrimaryTopicOf Maxwells_theorem.