TITLE: Is there a simple method to do LU decomposition by hand?
QUESTION [8 upvotes]: Today my professor in numerical analysis pointed out that in the exam we will probably have to do LU decomposition by hand.
I understand how the decomposition works theoretically, but when it comes actually getting my hands dirty, I'm never sure, if I'm writing the row operation at the right place in the L matrix.
Do you know a mnemonic, which allows one to efficiently compute the LU decomposition by hand?

REPLY [7 votes]: If you remember how to do Gaussian elimination, you can just do that -- the $U$ matrix is precisely the upper triangular matrix you get from elimination, and each subdiagonal entry $L_{ij}$ of $L$ is the multiple of row $j$ you subtract from row $i$ to zero the element $A_{ij}$. The diagonal entries are just the scaling factors to give unit diagonal for $A$. 
In fact, performing Gaussian elimination on the matrix in Sujaan Kunalan's example and comparing your steps with those in the example is probably a good way of getting a feel for the method (and more useful than memorizing indices).