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Derivation of Cholesky Decomposition

  • #1

Homework Statement


Derive Cholesky Decomposition for a 3x3 matrix

Homework Equations


IN: S is Real matrix with dimensions 3x3 and is Symmetric and semi-definite
Out: L is a Real matrix with dimensions 3x3 such that
  1. S=L*L^t
  2. L is lower-triangular

The Attempt at a Solution


We learned this in class, and here is what I have in my notes. Near the end, it starts not making sense, so I think I recorded something wrong, and I also don't fully get what's going on.

upload_2016-3-13_18-6-41.png
 

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Answers and Replies

  • #2
andrewkirk
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You have miscopied the subscripts in the second last line. Replace ##L_{32}## by ##L_{33}##, ##L_{21}## by ##L_{22}## and ##L_{31}## by ##L_{32}## and then it will follow from the line above.
 
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  • #3
You have miscopied the subscripts in the second last line. Replace ##L_{32}## by ##L_{33}##, ##L_{21}## by ##L_{22}## and ##L_{31}## by ##L_{32}## and then it will follow from the line above.
Thank you so much! You're a life saver. This got me so confused. QR decomposition just clicked for me about 5 minutes ago, and now I get this too!
 

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