Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Singular Value Decomposition

Chapter 4 Linear algebra

Chapter 4: QR Decomposition and Numerical Rank — Pivoting QR & SVD (also appears in Ch. 8)

High-resolution PNG
Singular Value Decomposition — high-resolution mind-map icon

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

Open Chapter 4 companion →

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 ().