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Eigenvalues of n x n matrix

  1. Mar 4, 2009 #1
    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?
     
  2. jcsd
  3. Mar 4, 2009 #2
    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.
     
  4. Mar 4, 2009 #3

    lurflurf

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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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