- Thread starter
- #1

- Apr 13, 2013

- 3,718

I have also an other question about the proof of the Cholesky decomposition.

We write A like that:

$A=\begin{bmatrix}

d & u^{T}\\

u & H

\end{bmatrix}=\begin{bmatrix}

\sqrt d & 0\\

\frac{u}{\sqrt d} & I_{n-1}

\end{bmatrix}\begin{bmatrix}

1 & 0\\

0 & K

\end{bmatrix}\begin{bmatrix}

\sqrt d & \frac{u^{T}}{\sqrt{d}}\\

0 & I_{n-1}

\end{bmatrix}$

where $K=H-\frac{1}{d}uu^{T}$

and then we suppose that $K$ is symmetric and positive-definite,to use the assumption step(that is valid for $(n-1)x(n-1)$ symmetric and positive-definite matrices.

But...then I have to prove that $K$ is positive-definite.How can I do this?