Suppose the matrix A is positive semidefinite and singular, with rank n−1. Will Cholesky factorization run to completion? Verify your conclusions from Exercise 3.13 by factoring the multinomial...

Suppose the matrix A is positive semidefinite and singular, with rank n−1. Will Cholesky factorization run to completion?

Verify your conclusions from Exercise 3.13 by factoring the multinomial covariance matrix diag(p1,...,pn) − ppT, where pT = (p1,...,pn) with n = 4 and probabilities (.4, .3, .2, .1).