Jordan canonical form theorem
A Jordan block or Jordan matrix is a matrix of the form
with a constant value along the diagonal and 1’s on the superdiagonal. Some texts the 1’s on the subdiagonal instead.
Theorem.
Let be a finite-dimensional vector space over a field and be a linear transformation. Then, if the characteristic polynomial factors completely over , there will exist a basis of with respect to which the matrix of is of the form
where each is a Jordan block in which .
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 |