Jordan canonical form theorem

A Jordan blockMathworldPlanetmath or Jordan matrix is a matrix of the form


with a constant value λ along the diagonal and 1’s on the superdiagonal. Some texts the 1’s on the subdiagonal instead.


Let V be a finite-dimensional vector spaceMathworldPlanetmath over a field F and t:VV be a linear transformation. Then, if the characteristic polynomialMathworldPlanetmathPlanetmath factors completely over F, there will exist a basis of V with respect to which the matrix of t is of the form


where each Ji is a Jordan block in which λ=λi.

The matrix in Theorem 1 is called a Jordan canonical form for the transformation t.

Title Jordan canonical form theorem
Canonical name JordanCanonicalFormTheorem
Date of creation 2013-03-22 12:59:21
Last modified on 2013-03-22 12:59:21
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 16
Author Mathprof (13753)
Entry type Theorem
Classification msc 15A18
Synonym Jordan canonical form
Related topic PartitionedMatrix
Related topic SimultaneousUpperTriangularBlockDiagonalizationOfCommutingMatrices
Related topic Diagonalizable2
Defines Jordan block
Defines Jordan matrix