= LQ decomposition
{c}
{title2=$A=LQ,\quad QQ^T=I$}
An <LQ decomposition> factors a real $m\times n$ matrix into a lower trapezoidal $m\times n$ matrix $L$ and an orthogonal $n\times n$ matrix $Q$. Transposing a <QR decomposition> of $A^T$ proves existence. Equivalently, right <Householder transformations> clear the part of each row beyond its diagonal while preserving earlier zeros. This factorization is useful for underdetermined systems, complementing the role of <QR decomposition> in overdetermined systems.
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