Diagonalization

Now that we know about eigenvalues and eigenvectors, we are ready to learn about diagonalization. This involves writing a matrix as a product of other matrices, one of which is a diagonal matrix, with values only along the main diagonal. This has many applications in computation, so let's take a look!

Script by Howard Whittle

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[Dan-jqeq]

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[greendino]

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[noellelavenza]

My professor hasn't lectured all semester and just pointed us at the textbook, and this was the last topic I didn't fully get on my own before our exam today. You're a lifesaver.

[Prof.afterMATH]

This is always a hard topic to teach. This is straight forward and clear. Great video!

[fizzy]

I have a PhD in math but professor Dave is so much more well rounded than myself. He's doing matrix algebra here and I'm using his videos to get the gist of population evolution and abiogenesis.

[youtubecubedude]

Prof Dave is great at teaching, but it’s really the editing that makes these videos so easy to understand.

[ephemeronchimera]

Prof Dave: I am currently doing self-study of every math course required for an undergraduate math program and I was having a hell of a time understanding fully how to perform diagonalization! I have read countless textbooks' sections on diagonalization and watched several other videos. I took thorough notes from your mini lecture, followed along with you on the example and am stoked to say I was able to go through the example problem at the end and got everything right. ALSO...nowhere else has anyone mentioned to ALWAYS choose x2=1. That tiny detail helped make everything else click and I agree with you that the process of diagonalization is in fact easy, albeit time-consuming. I cannot thank you enough for this! The way you go through and show every single detail is a TREMENDOUS help! I really appreciate you!

[nolapickering]

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[conzopontsho]

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T - 7:17:00 until the exam, thank you! Learned what was chaotically taught in two weeks in under two hours with notes taken and examples calculated by watching two of your videos. The 222 (*3 :])

[kevingarza]

This definitely simplified everything that was taught to me in my class lecture. Everything is super clear now. Thank you so much!

[TenaciousDanR]

Great video! This helped me so much. I know this is a little late but I just wanted to point out that instead of calculating X inverse to check your answer at the end, you can simply check to see if AX = XD . This is much easier if you are asked a similar question that uses nxn matrices where n > 2 as the computing the inverse becomes more annoying as n increases.

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[mohsen]

thank you professor.
every teacher must see you videos first to be qualified for teaching