An Hermitian matrix [tex] H [/tex] is positive definite if all its eigenvalues are nonzero and positive. Assume that the matrices [tex] A,B [/tex] are positve definite, and that the difference [tex] A-B [/tex] is positve definite. Now, for which unitary matrices, [tex] U [/tex], is it true that the matrix [tex] A-UBU^{\dagger} [/tex] is positve definite.
I haven't been able to solve this problems, and I'm not sure if it is because it is to difficult (i.e. the only way to solve it is to check for all [tex] U [/tex]) or because I'm to incompetent. Any suggestions would be appreciated.
/David
I haven't been able to solve this problems, and I'm not sure if it is because it is to difficult (i.e. the only way to solve it is to check for all [tex] U [/tex]) or because I'm to incompetent. Any suggestions would be appreciated.
/David