Could anyone tell me how he has defined $\pi$? what are $w_i,v_i$? there is no indigation of them before.
I though that if $v=[v_1,\dots,v_n]^T. w=[w_1,\dots,w_n]$ then $\pi=[\frac{v_1}{w_1},\dots,\frac{v_1}{w_1}]$ but it is also a column vector, then what does he meant with diagonal of $\pi$? and what may be $\pi_i$?
Thanks for the help.
$v$ and $w$ are each column vectors. The $i$th component of $v$ is denoted $v_i$, and the $i$th component of $w$ is denoted $w_i$.
$\pi$ is a column vector whose $i$th component is $\pi_i := w_i / v_i$.
$\text{diag}(\pi)$ is notation for a $n \times n$ diagonal matrix, whose $i$th diagonal entry is $\pi_i$.