If A is a $m\times n$ matrix $m\geq n$,A=QR is a reduced QR factorization. If R has k nonzero diagonal entries ($0\leq k
The rank of QR factorization
0
$\begingroup$
linear-algebra
numerical-methods
-
0There seems to be a typo -- you probably want to know the rank of something other than $k$? – 2012-09-19
1 Answers
2
$A=QR=[Q_1,Q_2]\begin{bmatrix}R_1 \\ 0\end{bmatrix}=Q_1R_1$
Since $Q_1$ has full column rank, so $\operatorname{rank}(A)=\operatorname{rank}(Q_1R_1)=\operatorname{rank}(R_1)=k$.
See here for more info.