Schur decomposition
If is a complex square matrix of order n (i.e. ), then there exists a unitary matrix
such that
where is the conjugate transpose, (the are eigenvalues
of ), and is strictly upper triangular matrix
. Furthermore, can be chosen such that the eigenvalues appear in any order along the diagonal. [GVL]
References
- GVL Golub, H. Gene, Van Loan F. Charles: Matrix Computations (Third Edition). The Johns Hopkins University Press, London, 1996.
Title | Schur decomposition![]() |
---|---|
Canonical name | SchurDecomposition |
Date of creation | 2013-03-22 13:42:12 |
Last modified on | 2013-03-22 13:42:12 |
Owner | Daume (40) |
Last modified by | Daume (40) |
Numerical id | 8 |
Author | Daume (40) |
Entry type | Theorem |
Classification | msc 15-00 |
Related topic | AnExampleForSchurDecomposition |
Related topic | ProofThatDetEAEoperatornametrA |