Compute large powers of a matrix via diagonalization

Description: As an example of the benefits of diagonalization, we see how taking a large power of a matrix is quick and easy when you can diagonalize a matrix.

Learning Objective: Compute powers of a matrix quickly via diagonalization

This video is part of a Linear Algebra course taught by Dr. Trefor Bazett at the University of Cincinnati

[elanadavis]

shoutout to you for teaching me linear algebra

[amkhrjee]

It would be great if you could rearrange the order of videos in the playlist. This one and the one before should definitely come after the similarity video. And as always, the videos are great!

[MrJapogm]

Masterful . I really appreciate this video.

[Angry-est]

Saved my bacon, my brain was not comprehending this until now. 😅

[Fallen]

You should rearrange the playlist... This video is ranked before similarity.

[peterlingas]

What if it is not diagonalizable? Say for example:

[ 1 -4 2 ]
A = [ 0 -3 2 ]
[ -1 -1 1 ]
with eigenvalues 1 and -1?
and eigenvectors [-1, 1, 2] and [1, 1, 1]

How would you then find A^n?