Symmetric positive definite

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Homework Statement


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)



Homework Equations




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
BvU
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I' m asked to solve this question using Choelsky method
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 !
 
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question solved
 

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