If the n × n matrix A has real entries, its complex eigenvalues will always occur in complex conjugate pairs. Thus, say, if a 7 × 7 matrix with real entries has 8,3+2i,−2 − 5i and −3i as eigenvalues, we know that automatically the remaining eigenvalues are 3 − 2i,−2+5i and 3i.
Can eigenvalues be complex number?
Since a real matrix can have complex eigenvalues (occurring in complex conjugate pairs), even for a real matrix A, U and T in the above theorem can be complex.
How do you find complex eigenvalues?
Let A be a 2 × 2 real matrix.
- Compute the characteristic polynomial. f ( λ )= λ 2 − Tr ( A ) λ + det ( A ) , ...
- If the eigenvalues are complex, choose one of them, and call it λ .
- Find a corresponding (complex) eigenvalue v using the trick.
- Then A = CBC − 1 for.
