# Symmetric positive definite

1. Feb 24, 2017

### fonseh

1. The problem statement, all variables and given/known data
Here's the question :
1x1+ 2x2 +0x3 + 0x4 = 1
2x1+ 9x2 +1x3 + 0x4 = 6
0x1+ 1x2 +9x3 + 4x4 = 2
0x1+ 0x2 +4x3 + 3x4 = 8

I' m asked to solve this question using Choelsky method ( We need the symmetric positive definite matrix when we are using this method)

2. Relevant equations

3. The attempt at a solution
matrix A = $$\begin{bmatrix} 1 & 2& 0 & 0 \\ 2 & 9 & 1 & 0 \\\ 0 & 1 & 9 & 4 \\ 0 & 0 & 4 & 3 \end {bmatrix}$$

the book stated that for the positive symmetric matrix , we need to ensure that max a_kj less than max a_ii ,
But , in this example , i found that the a_44 which is 3 is less than a_43 which is 4 ... So , how could this be symmetric positive definite matrix ?
How is it possible to solve using Choelsky method ?

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2. Feb 24, 2017

### BvU

The guy is called Cholesky.

But it's clear what you are being asked, so go to work and see if and where it goes wrong !

3. Feb 24, 2017

### fonseh

question solved