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Householder Elimination

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For a non-singular matrix $ A$, the matrix equation

$\displaystyle AX=B

can be solved with the aid of the QR factorization

$\displaystyle A(:,I)=QR \,.

We have

$\displaystyle QR X(I,:)=B \quad \Longleftrightarrow \quad R \underbrace{X(I,:)}_Y =Q^t B \,.

Hence, $ Y=X(I,:)$ can be determined via backward substitution.
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  automatically generated 7/ 2/2007