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ExtremeBDS [4]
2 years ago
8

2. Prove that a 3x3 matrix must have at least one real eigenvalue. Is it important, as part of the proof, to find this eigenvalu

e? Why or why not?
Mathematics
1 answer:
Harlamova29_29 [7]2 years ago
4 0

A 3x3 matrix has a characteristic polynomial of degree 3. If all the elements of the matrix are real, then the polynomial has up to 3 distinct complex roots. If one of these roots is complex (in particular, has a non-zero imaginary part), then a second root would be that first root's complex conjugate. Then the remaining root has to be real.

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