MathDB

Let

A

and

B

be complex Hermitian

2\times2

matrices having the pairs of eigenvalues

(\alpha_1,\alpha_2)

and

(\beta_1,\beta_2)

, respectively. Determine all possible pairs of eigenvalues

(\gamma_1,\gamma_2)

of the matrix

C=A+B

. (We recall that a matrix

A=(a_{ij})

is Hermitian if and only if

a_{ij}=\overline{a_{ji}}

for all

i

and

j

Problem Statement