How to find $$||A - QR||_2$$ without finding Q matrix
(A is matrix, QR - qr decomposition of A)
I have written a code which return only R (using Householder transformation).
2026-03-29 20:46:32.1774817192
QR decomposition error
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If you've found the QR decomposition for A, then $A=QR$, hence the norm of their difference is 0.
If you're solving the Least Squares problem minimizing $||Ax - b||_2$ then the error, or residual, is the norm of the last m-n elements of the vector $Q^Tb$.