Ex10 16

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 10.16}$

Show that the vector of ordered eigenvalues $\lambda^\psi$ for the density operator of any unentangled state $\ket\psi$ of a bipartite system majorizes the vectors for any other state of the bipartite system.