Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online lexicon: Annotation to

Diagonalization of Cyclic Matrices

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview
A cyclic $ n\times n$-matrix $ A$ can be diagonalised by means of Fourier matrix

$\displaystyle W = (w^{jk})_{j,k=0,\ldots,n-1}, \quad w = \exp(2\pi\mathrm{i}/n)\, : $

$\displaystyle \frac{1}{n} \overline{W} \left(\begin{array}{cccc} a_0 & a_{n-1... ...\vdots & \ddots & \vdots \\ 0 & \cdots & \lambda_n \end{array}\right)\, , $

where

$\displaystyle \lambda_\ell = \sum_{k=0}^{n-1} a_k w^{-k'\ell},\quad \ell=0,\ldots,n-1 $

are the eigenvalues of $ A$.

(temporary unavailable)
[Back]
  automatisch erstellt am 19.  8. 2013