# Cholesky factorization of a block matrix

Let a Matrix $\mathbf{Y=[A\;b;b^T\;}d]$, where $d$ is a scalar, and $\mathbf{b}$ is a vector. How to find the cholesky factorization of $\mathbf{Y}$ if i know the cholesky factorization of $\mathbf{A}$.?

• Welcome to SciComp.SE! This is called an update of the Cholesky factorization; you can find a discussion in many textbooks and papers as well as at math.stackexchange.com/questions/955874/…. – Christian Clason Oct 21 '15 at 7:52
• @ChristianClason Thanks for the link. Additionally can we update the cholesky factorization of A1=[A a] after a column addition? – Astro Oct 21 '15 at 8:34
• No, because the matrix $A1$ needs to be symmetric and positive definite for a Cholesky factorization to exist, and adding a column without adding a row leads to a non-square matrix which can't be symmetric. – Christian Clason Oct 21 '15 at 8:38
• @ChristianClason Oh! My bad. sorry i intended to ask something else. Anyway i got the answer from the link you sent. – Astro Oct 21 '15 at 8:44