Permuted LU Decomposition
Chapter 5: Square Matrix and LU Decomposition — PLU Decomp ($PA = LU$)
From the book
Chapter 5: Square Matrix and LU Decomposition. In the chapter mind map this icon labels PLU Decomp ($PA = LU$). The discussion below is excerpted and lightly edited from § PLU Decomposition (Pivoted LU) in Mathematics for AI and Machine Learning.
LU decomposition requires that all leading principal minors are non-zero and is typically limited to square matrices. PLU decomposition (Pivoted LU) generalizes LU decomposition: it works for ANY rectangular matrix $A \in \mathbb{R}^{M \times N}$ and ALWAYS exists (via row permutation $P$ for numerical stability).
What this drawing shows
What you see. Shows pivoting as a permutation applied before LU factorization for numerical stability.
In the mind map. Chapter 5 — PLU 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 5: Square Matrix and LU Decomposition — see the mind-map node PLU Decomp ().