We model the web by a directed graph with $n$ vertices. The matrix $A$ is the stochastic matrix described in question 29. We define $$B = ( 1 - \alpha ) A + \frac { \alpha } { n } J _ { n }$$ where $J _ { n }$ is the matrix in $\mathcal { M } _ { n } ( \mathbb { R } )$ whose coefficients are all equal to $1$, $A$ is the stochastic matrix described in question 29 and $\alpha$ is a real number in $] 0,1 [$, called the damping factor. Show that $B$ is a stochastic matrix whose coefficients are all strictly positive.
We model the web by a directed graph with $n$ vertices. The matrix $A$ is the stochastic matrix described in question 29. We define
$$B = ( 1 - \alpha ) A + \frac { \alpha } { n } J _ { n }$$
where $J _ { n }$ is the matrix in $\mathcal { M } _ { n } ( \mathbb { R } )$ whose coefficients are all equal to $1$, $A$ is the stochastic matrix described in question 29 and $\alpha$ is a real number in $] 0,1 [$, called the damping factor.
Show that $B$ is a stochastic matrix whose coefficients are all strictly positive.