- #1

fanxiu

- 3

- 0

**1. Let A**

^{H}be the hermitian matrix of matrix A, and how the eigenvalues of A^{H}be related to eigenvalues of A?**3. what I have done is**

equation no.1: (A

And equation no.2: (A-r

time no.1 both sides by x

((A*x

Then we have (conjugate (r

only if x

conjugate (r

so i just reach this conditional conclusion. but i am not sure what else can be know about the eigenvalues of hermitian matrix

equation no.1: (A

^{H}-r_{1}*I) * x_{1}= 0,And equation no.2: (A-r

_{2}*I) * x_{2}= 0time no.1 both sides by x

_{2}^{H}((A*x

_{2})^{H}-r_{1}*x_{2}^{H})* x_{1}= 0Then we have (conjugate (r

_{2}) -r_{1})*x_{2}^{H}*x_{1}= 0only if x

_{1}and x_{2}^{H}are not orthogonal vectors,conjugate (r

_{2}) = r_{1}so i just reach this conditional conclusion. but i am not sure what else can be know about the eigenvalues of hermitian matrix