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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