1. Assume is a real matrix with a complex eigenvalue and is an associated eigenvector. If is the complex conjugate of show that is an eigenvector of associated with eigenvalue 2. 7 Prove that...

1. Assume

is a real

matrix with a complex eigenvalue

and

is an associated eigenvector. If

is the complex conjugate of

show that

is an eigenvector of

associated with eigenvalue

2. 7 Prove that

and

^T
have the same eigenvalues. Hint: By Problem 4.19, det
det

^T

Apply this result to the characteristic equation of

Problem 4.19