Singular Value Decomposition
Chapter 4: QR Decomposition and Numerical Rank — Pivoting QR & SVD (also appears in Ch. 8)
From the book
Chapter 4: QR Decomposition and Numerical Rank. In the chapter mind map this icon labels Pivoting QR & SVD. The discussion below is excerpted and lightly edited from § Opening in Mathematics for AI and Machine Learning. Related material also appears in Chapter 8 ($A = U\Sigma V^\top$).
QR decomposition and matrix rank: orthonormal bases and linear independence
What this drawing shows
What you see. Shows a matrix as rotations/reflections plus axis-aligned stretching.
In the mind map. Chapter 4 — Pivoting QR & SVD. See From the book above for definitions, figures, and worked examples.
Also appears in Ch. 8 ().
Where to read next
Read the full definitions, figures, and worked examples in Chapter 4: QR Decomposition and Numerical Rank — see the mind-map node Pivoting QR & SVD.
This concept is also referenced in Chapter 8 ().