$B_{(n+1)(n+1)}$ = $ \begin{bmatrix} A & u \\ u^T & 1 \\ \end{bmatrix}$
is given, and $A$ is a positive definite matrix where its Cholesky factorization is given by $A=L*L^T$ formula. $A$ is $n\times n$ matrix and $u$ is a n_vector.
Now assuming $\|L\|^{-1}\leq 1$, I need to show that $B$ is a positive definite for all $\|u\|<1$.
Thanks