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?


2 Answers 2


Note that I didn't write this answer; taken from: LU Decomposition Steps

This is also useful: Upper and Lower Triangular Matrices

Let's go step by step. We want an equation of the following form: (An example is given below)


From the first column and first row of our known matrix, it's not too hard to see that we can start with this:


Next, we can choose the diagonal elements of our upper triangular matrix to be $1$, and fill in the lower triangular matrix column by column:




  • $\begingroup$ how about non square matrices? $\endgroup$
    – mahdi
    Mar 29, 2018 at 6:45

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).


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