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Mathematics-Online problems:

Interactive Problem 1139: Eigenvalues and Inverse of a Cyclic 4x4 Matrix


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

Determine the eigenvalues and the inverse of the cyclic matrix

$\displaystyle A=\left(\begin{array}{cccc}
0 & 1 & 3 & 1 \\
1 & 0 & 1 & 3 \\
3 & 1 & 0 & 1 \\
1 & 3 & 1 & 0 \\
\end{array}\right)
$

by using the discrete Fourier transform.

Answer:

Eigenvalues:          , , , .

(In ascending order; multiple results, if applicable.)

First row of the inverse matrix:          , , , .

(The results should be correct to four decimal places.)


   

see also:


  automatically generated: 8/11/2017