Question

Can we do A = LU decomposition of a matrix in which we encounter that the current pivot turns out to be zero in the middle of elimination? If no, then why not?

Answer 1

lokeshh, are you allowing a reordering of the rows along with your LU decomposition, ie, PA=LU? If not then I don't think you can proceed if you hit a zero in the pivot positions while there are still non-zeroes left below. But if you allow the use of a permutation matrix then you should be able to proceed by swapping the row with a zero in the pivot position with a lower row. When I was doing this in the exercises I found it hard to avoid having to start again whenever P changed---but perhaps with careful management there's a way of updating L whenever you change P. Josh.

Answer 2

Thanks got it.

Answer 3

Just one more thing. Can invertible matrices have LU decomposition?

Answer 4

Yes, for sure: invertible matrices will have a full set of pivots ( no zeros), so you shouldn't have to worry about P.