Module 04 / §3.12–3.17
SVD & matrix tools
Connect subspaces, matrix norms, low-rank approximation, and pseudoinverses.
6 lessons · Visual explanations · Guided experiments
04.1 / Explore → understand → practice
What does a matrix stretch?
Follow orthogonal changes of coordinates and singular-value scaling, including rectangular matrices.
04.2 / Explore → understand → practice
Which part of an input survives?
Decompose inputs and outputs into the four fundamental subspaces.
04.3 / Explore → understand → practice
How much can a matrix amplify a vector?
Compare induced norms, Frobenius size, and orthogonal invariance.
04.4 / Explore → understand → practice
How much can you discard?
Use truncated SVD and prove its spectral-norm optimality.
04.5 / Explore → understand → practice
Can you undo a map that loses information?
Construct the Moore–Penrose pseudoinverse and verify its four conditions.
04.6 / Explore → understand → practice
How do columns and outer products build a matrix?
Translate matrix products and quadratic forms into sums of entries.