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Both algorithm return very similar results in terms of having a upper/right triangular matrix as one of the factors.

What is the relationship between Q and L, and between R and U? What is the intuition behind this relationship?

mymindcastadrift
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    There isn't really any relationship. About all I can say is that (in the real, invertible case) the systems $Rx=Q^Tb$ and $Ux=L^{-1}b$ are both triangular linear systems which are equivalent to $Ax=b$. But there is not, for instance, a quick way to get a QR factorization from an LU factorization or vice versa. – Ian Jul 03 '15 at 20:38

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