The Jordan Normal Form Theorem states that every square matrix over an algebraically closed field is similar to a matrix in Jordan normal form, a block-diagonal matrix whose blocks each carry a single eigenvalue on the diagonal with ones directly above it. Named for Camille Jordan, it gives the finest general classification of linear operators up to similarity available over such a field.
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StatementFor a linear operator on a finite dimensional vector space over an algebraically closed field, there exists a basis in which the operator's matrix takes Jordan normal form: a block diagonal matrix whose blocks each carry one repeated eigenvalue along the diagonal, ones on the entries immediately above the diagonal, and zeros everywhere else. 1 Proof YearCamille Jordan first stated the Jordan decomposition theorem in 1870. Karl Weierstrass had proved an equivalent classification independently in 1868, unknown to Jordan at the time. Classification
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1. Jordan Normal Form Theorem (Wikipedia)
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The Jordan normal form is named after Camille Jordan, who first stated the Jordan decomposition theorem in 1870.
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