I have a probability vector $p$ s.t. $1^Tp=1$ and $p\geq 0$.
I want to compute the spectral radius of the matrix $M=\text{diag}(p)-pp^T$ where $\text{diag}(p)$ has its diagonal elements as $p$ and its off-diagonals as 0.



What is the spectral norm of the matrix $\text{diag}(p)-pp^T$?
A more general problem is addressed in section 5 of [Golub, G. H. "Some modified matrix eigenvalue problems". *SIAM Review* **15**, 318 (1973)](https://doi.org/10.1137%2F1015032).


For background and other references see the Wikipedia article on the [Bunch-Nielsen-Sorensen formula](https://en.wikipedia.org/wiki/Bunch%E2%80%93Nielsen%E2%80%93Sorensen_formula).


