Add a new notebook 60_linear_algebra_2/230_QR_Method_Eigenvalues.ipynb between Power Method (200) and Jacobi (240), covering the QR algorithm for general (possibly non-symmetric, possibly complex-eigenvalued) matrices.
Code scope (Scope B from IMPROVEMENTS.md)
- Basic QR iteration:
Aₖ₊₁ = Rₖ Qₖ with shift-free demonstration.
- Real Schur form with 2×2 diagonal blocks for complex conjugate eigenpairs.
- Slider over iteration step + Hinton diagram of
Aₖ showing the upper-triangularization.
Explanation scope (the deliverable that gates the merge)
The advanced-topic-policy gating criterion is teachability. Author the following:
- Why QR works — informal: each iteration is a similarity transformation that systematically pushes mass into the upper triangle. Connection to Power Method — QR is "subspace iteration" applied to all columns at once.
- Why complex eigenvalues become 2×2 real blocks — a real matrix cannot have a single real diagonal entry equal to a complex eigenvalue; the conjugate pair lives as the eigenvalues of a 2×2 sub-block.
- What "real Schur form" means vs the complex Schur form, and why textbooks usually show the real version.
- Convergence behavior — geometric rate driven by eigenvalue ratio; why a shift accelerates it (mention without implementing if Scope B).
- Where this sits in the curriculum — reading Power Method (
200) as "find one eigenvector" and Jacobi (240) as "diagonalize a symmetric matrix"; QR fills the gap of "find all eigenvalues of a general matrix".
Note on policy
This is a brand-new notebook on an advanced topic. Per feedback_nmisp_teach_what_you_know.md, brand-new advanced material is mergeable only if the explanatory scaffolding is part of the same PR — not deferred to "we'll write the prose later."
Add a new notebook
60_linear_algebra_2/230_QR_Method_Eigenvalues.ipynbbetween Power Method (200) and Jacobi (240), covering the QR algorithm for general (possibly non-symmetric, possibly complex-eigenvalued) matrices.Code scope (Scope B from IMPROVEMENTS.md)
Aₖ₊₁ = Rₖ Qₖwith shift-free demonstration.Aₖshowing the upper-triangularization.Explanation scope (the deliverable that gates the merge)
The advanced-topic-policy gating criterion is teachability. Author the following:
200) as "find one eigenvector" and Jacobi (240) as "diagonalize a symmetric matrix"; QR fills the gap of "find all eigenvalues of a general matrix".Note on policy
This is a brand-new notebook on an advanced topic. Per
feedback_nmisp_teach_what_you_know.md, brand-new advanced material is mergeable only if the explanatory scaffolding is part of the same PR — not deferred to "we'll write the prose later."