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Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra

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Further reading 1

What does a matrix do, and which outputs can disappear? →Read a column as an arrow, then a matrix as an action on that arrow. Solving an equation becomes a question about reachable targets, giving collapse, eigenvectors and rotations a geometric interpretation.This video helps answer · Which outputs disappear when a transformation collapses space?

Caption notes

An eigenvector stays on its own line. Finding when A−λI collapses a dimension gives the eigenvalue condition; an eigenbasis simplifies repeated transformations.

Original passages · 4
some special vectors do remain on their own span
Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra · ▶ 1:57–2:07
make this determinant zero, meaning the tweaked transformation squishes space into a lower dimension
Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra · ▶ 7:58–8:07
what you have found is the axis of rotation
Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra · ▶ 4:11–4:20
change to an eigenbasis, compute the 100th power in that system, then convert back
Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra · ▶ 16:02–16:15

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