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Math Help - qr factorization

  1. #1
    Junior Member
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    qr factorization

    A =\left(<br />
\begin{array}{cc}<br />
1 & 3 \\<br />
2 & 4 \\<br />
-1 & -1 \\<br />
0 & 1 <br />
\end{array}<br />
\right)<br />

    Q = \left(<br />
\begin{array}{cc}<br />
1/\sqrt{6} & 1/\sqrt{3}\\<br />
2/\sqrt{6} & 0\\<br />
-1/\sqrt{6} & 1/\sqrt{3}\\<br />
0 & 1/\sqrt{3}<br />
\end{array}<br />
\right)<br />

    The columns of Q were obtained by applying the Gram-Schmidt Process to the columns of A. Find the upper triangular matrix R such that A=QR

    Now I'm pretty sure that R=Q^TA could someone please verify this and show what they got for R thanks
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  2. #2
    A Plied Mathematician
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    Your candidate for R will certainly imply that the equation A=QR holds. The columns being orthonormal (as they are, by inspection), implies that QQ^{T}=I, and Q^{T}Q=I. Those are differently sized identity matrices, of course.

    What I don't know off-hand is whether your candidate R is upper triangular. Why don't you post your calculations, and I'll verify those? (That's more in the spirit of this forum anyway!)
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