QR Factorization of A: Simple Procedure

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SUMMARY

The discussion focuses on the QR factorization of the matrix A = {{1, 1}, {-1, 1}}. The user seeks to find matrices Q and R such that A = QR, where Q is orthogonal and R is upper triangular. The user attempts to define Q and R but encounters issues with the non-zero entry in the lower left of matrix P when using Mathematica. The solution involves using the Gram-Schmidt orthonormalization process to derive Q and subsequently record the coefficients to obtain R.

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rbwang1225
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Homework Statement


Find the QR factorization of A = {1, 1}, {-1, 1}

The Attempt at a Solution


I just don't know the procedure.
I know it means that I need find Q and R such that A=QR, Q be orthogonal, and R be upper triangular.
It may be solved by assign Q = {a, b},{c, d}, where ##Q^TQ=1##
and P = {e, f}, {0, g}
But, as I run Mathematica, it gives me P that the left-down side entry is nonzero.
Is there any point that I misunderstood?
And is there any way to simplify the procedure?
P.S. Please forgive me that I don't know how to "type" a matrix.
Regards.
 
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Q is obtained by Schmidt othnormalization, record the coefficients to get R.
 

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