References: Eigenvectors and eigenvalues

Source material

Source curriculum (structural mirror, cited as further study):
• 3Blue1Brown, Essence of Linear Algebra, Chapter 14: "Eigenvectors and eigenvalues"
  Creator: Grant Sanderson
  Lesson page: https://www.3blue1brown.com/lessons/eigenvalues
  Series index: https://www.3blue1brown.com/?topic=linear-algebra
  License: copyright Grant Sanderson; videos published on his site and YouTube
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Watch this next

• Eigenvectors and eigenvalues (3Blue1Brown) by Grant Sanderson. The video this lesson mirrors. Watching a vector swept around the circle while its transformed image snaps onto the same line at the eigenvector directions is the single clearest way to internalize what an eigenvector is. The diagonalization payoff is also animated. About seventeen minutes, the longest in the series, and worth every minute.

Going deeper

• Essence of Linear Algebra (full series) by 3Blue1Brown. The series this track follows. The inverses chapter underwrites the characteristic equation (zero determinant means a nontrivial null space), and the change-of-basis chapter set up the diagonalization this lesson delivers; the next (Abstract vector spaces) steps back from arrows entirely.

• Khan Academy: Linear algebra for a slower, exercise-driven treatment of eigenvalues, eigenvectors, and the characteristic equation, with practice problems and immediate feedback.

Adjacent topics

Where this sits in the track.

• Inverses and change of basis (earlier lessons). Eigenvectors sit at the intersection of two earlier ideas: the characteristic equation det(M - λI) = 0 is the inverses lesson’s collapse condition, and the diagonalization D = P^-1 · M · P is the change-of-basis sandwich applied to the basis the transformation prefers.

• Abstract vector spaces (next lesson). Everything in this track, vectors, transformations, eigenvectors, has been about arrows and grids. The final lesson asks which of these ideas survive when “vector” means a function or a polynomial, objects that can be added and scaled but are not arrows at all.