Truncated SVD
Chapter 4: QR Decomposition and Numerical Rank — Numerical $\epsilon$-Rank (also appears in Ch. 8)
From the book
Chapter 4: QR Decomposition and Numerical Rank. In the chapter mind map this icon labels Numerical $\epsilon$-Rank. The discussion below is excerpted and lightly edited from § Numerical Rank Computation in Mathematics for AI and Machine Learning. Related material also appears in Chapter 8 (Truncated SVD: Rank-$k$ Approx).
In practice, computing the exact rank of a matrix is challenging due to floating-point arithmetic. Small numerical errors can make a rank-deficient matrix appear full rank, or vice versa.
What this drawing shows
What you see. Shows keeping only the leading singular directions to form a low-rank approximation.
In the mind map. Chapter 4 — Numerical -Rank. See From the book above for definitions, figures, and worked examples.
Also appears in Ch. 8 (Truncated SVD: Rank- Approx).
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 Numerical -Rank.
This concept is also referenced in Chapter 8 (Truncated SVD: Rank- Approx).
