Related question: this topic is examined
Eigenvectors and Eigenvalues
Eigenvectors Ax = λx, checking eigenvalues by solving (A − λI)x = 0, eigenspaces, eigenvalues of triangular matrices, and independence of eigenvectors for distinct eigenvalues.
How to read this page
Every original slide is shown unchanged. Yellow marks on a slide point to a numbered note: hover or tap a mark to jump to its note, and hover a note to see its marks. Questions tagged Past exam appeared on a real paper; Prediction questions are likely angles, not confirmed. Pick an answer to each question: a wrong pick tells you why it is wrong, so you can try again.
CS 223: Computational Linear Algebra
Slide 2
Exam angle
Related question: this topic is examined
Related question: this topic is examined
Related question: this topic is examined
The zero vector can be an eigenvector.
- Eigenvectors are nonzero (but 0 can be an eigenvalue).
How to determine whether a given How to determine whether a given
Slide 4
Slide 5
Notes
Eigenspace of λ = Nul(A − λI); its dimension = number of free variables.
Slide 6
Eigenvalues of triangular matrix
Notes
Eigenvalues of a triangular matrix are its diagonal entries. 0 is an eigenvalue ⇔ A is not invertible. Eigenvectors for distinct eigenvalues are linearly independent.
Exam angle
The eigenvalues of [[3, 6, −8], [0, 0, 6], [0, 0, 2]] are:
Example:
