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Eigenvalues of n x n matrix

  • Thread starter coldstone
  • Start date
Just wondering is there a way to get the characteristic equation of an n by n matrix without going through tedious calculations of solving multiple determinants of matrices?
 
I think you're basically stuck using the determinant, but there are many ways to simplify a matrix so that calculating it's determinant is easier.
 

lurflurf

Homework Helper
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There are many ways
-Hamiltan-Cayley
Find powers of the matrix and find the polynomial they satisfy
-eigenvalues
The terms of the characteristic polynomial are home geneous combinations of the eigenvalues
p=(x-eigenvalue1)(x-eigenvalue2)(x-eigenvalue3)...
 

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