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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


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    Homework Helper

    There are many ways
    Find powers of the matrix and find the polynomial they satisfy
    The terms of the characteristic polynomial are home geneous combinations of the eigenvalues
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