Simple and to the point. Watched many videos about it and none were as concise and informative as yours. Thank you so much for helping me pass linear algebra.
Great explanation. We had a simulation of interconnected networks. With something on the order of 20 nodes and about as many pathways, we often ended up with 40 to 60 simultaneous equations, forming square matrixes of the that size. Fortunately we had a nice computer subroutine that did this same L-U decomposition with back-substitution. And yes, it had logic to look for zero in the pivots, perform those row swapping with an auxiliary array that kept track of such pivots. It was an impressive algorithm but just as you show, straight-forward.
Beautiful explanation. My only note here is that in case 2, you do not need to immediately adjust A after adjusting P. You've already done that by L and U. It's like L * U = P * A being 3 * 4 = 1 * 12. If you change P to 2, you don't go back and adjust A to 6. You adjust U from 4 to 8. So now it's 3 * 8 = 2 * 12.
very nice explanation but a mistake, at 19:19 u s y if u multiply the 2 matrices on left side u get what u multiply on right side. but u don't get that in there. The right most matrix should be the original matrix. the one which is right below the case 2.
