Linear Algebra - Lecture 40: Diagonalization and Large Matrix Powers

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We introduce diagonalization of a matrix, which we motivate via the problem of computing large matrix powers. We characterize diagonalization in terms of eigenvalues and eigenvectors, and then we use it to find formulas for arbitrary powers of some matrices.

Please leave a comment below if you have any questions, comments, or corrections.

Timestamps:
00:00 - Introduction and definition
04:47 - Characterization of diagonalizability
11:14 - Diagonalization example
14:17 - Large power example
18:00 - Complex large power example

#linearalgebra #eigenvaluesandeigenvectors #diagonalization #matrices #math
  1. Nathaniel Johnston
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I have been banging my head against this subject for the last 4 day's with little progress while studying for a test, Managed to finally get it thanks to this video!
Thank you so much for this video and series!

zoomerby
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Thank you for making me fall in love with Linear Algebra Dr. Johnston. You have a huge place in my MATH/CS journey. I wish I was still in MTA. Keep up the good work!

Optmzdlyz
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I noticed that the Amazon listening for your upcoming Advanced Linear Algebra text (which I'm excited about!) has been taken down on Amazon. Has the release been pushed back?

ryanj