$QR$ factorization: why $A$ and $R$ have the same rank

Question

In $A=QR$ factorization why $R$ has always the same rank of $A$?

Because $Q$ is invertible then it has a full-rank. – Jun 04 '14 at 14:02 — , Jun 04 '14 at 14:02

score 2 · Accepted Answer · answered Jun 04 '14 at 13:55

2

this is because $rank(AB) \le min\{rank(A), rank(B)\}$. This gives you an inequality one way, and you get the other way by inverting $Q$ and looking at $R = Q^{-1}A$

answered Jun 04 '14 at 13:55

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$QR$ factorization: why $A$ and $R$ have the same rank

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