# LU decomposition of banded matrix without pivot

Say I have a Matrix $$M$$ that is a banded matrix where an LU decomposition exists (so without pivot). Are the $$L$$ and $$U$$ of the $$LU$$ decomposition also banded? Is the band the same (ignoring the upper/lower bound for L/U)?

Yes, just think of computing $$LU$$ by doing Gaussian elimination.