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Find Eigenvalues without function "eig"

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Jaycie Bishop
Jaycie Bishop on 11 Oct 2020
Edited: KSSV on 12 Oct 2020
I performed this by hand and know that the eigenvalues are 10, -1, and 4. But clearly that's not what I got... Any help would be nice.

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Bruno Luong
Bruno Luong on 11 Oct 2020
correct value of x2 is 13 (not 7)

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Answers (2)

KSSV
KSSV on 11 Oct 2020
Edited: KSSV on 12 Oct 2020
syms x
A = [10 0 0; 1 -3 -7 ; 0 2 6] ;
p = det(A-eye(3)*x) % this is the characteristic equation
val = solve(p) % solve this for roots
The polynomial equation, you get is:
poly =
Using roots:
p = [-1 13 -26 -40] ;
val = roots(p)

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Paul
Paul on 11 Oct 2020
roots(poly(A))
Though I’m sure one could come with an A for which this approach will fail due to numerical accuracy issues. In which case converting A to a syms object as in another answer may be preferred.

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