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?
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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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