# LU Decomposition

1. Aug 20, 2009

### demipaul

How would I calculate the determinant of a square matrix using LU Decomposition. Please be plain, I am not good with technical terms. An example would be nice. Thank you!

2. Aug 20, 2009

### jeff1evesque

Hello,

I looked up a nice example on how to compute LU Decomposition. On this http://www.utdallas.edu/dept/abp/PDF_Files/LinearAlgebra_Folder/LU_Decomposition.pdf" [Broken], the author has provided a nice clear explanation on how to do an LU decomposition (I've also attached the pdf, in case the link is taken down).

And according to http://en.wikipedia.org/wiki/LU_decomposition#Determinant"
(Note: A http://planetmath.org/encyclopedia/UnitLowerTriangularMatrix.html" [Broken] is a triangular matrix with 1's along it's diagonals)

So if you used the methodology to get an LU decomposition and further reduce the L matrix to a lower triangular matrix with 1's along the diagonal- then you can simply take the product of the diagonals of the right upper triangular matrix U to get your determinant for matrix A.

#### Attached Files:

• ###### LU_Decomposition.pdf
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Last edited by a moderator: May 4, 2017