LQ Decomposition
From the book
Chapter 9: Matrix Decompositions and Beyond. In the chapter mind map this icon labels LQ Decomp: $A = LQ$. The discussion below is excerpted and lightly edited from § Theorem: LQ Decomposition in Mathematics for AI and Machine Learning.
For any matrix $A \in \mathbb{R}^{M \times N}$ with $\mathrm{rank}(A) = r$, there exists a decomposition
where $L \in \mathbb{R}^{M \times r}$ is lower triangular, and $Q \in \mathbb{R}^{r \times N}$ has orthonormal rows ($Q Q^\top = I_{r \times r}$).
What this drawing shows
What you see. Shows a matrix factored into a lower-triangular factor and an orthonormal factor, the row-oriented analogue of QR.
In the mind map. Chapter 9 — LQ Decomp. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 9: Matrix Decompositions and Beyond — see the mind-map node LQ Decomp.