Orthogonality and Orthonormality

We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one another. Beyond this, we must understand the term orthonormal, and why orthonormal sets of vectors are important. Let's check it out!

Script by Howard Whittle

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[pkasb]

I must say your lecture supercedes those in higher institutions.

[isxp]

Good god, I wish I found this 8 weeks ago. The drop date for classes is the 30th. I ended up with 6% on my first midterm in Mathematical Physics. This class will haunt till the day I die. I'll probably know this material better than any of the classes I've taken, as I'll likely obsess over it for months.

[tadabae]

my final exam is in 15 minutes and i stumbled across this channel. he explains this so clearly!! i wish i found this channel earlier omg

[lingwaili]

Thank you so much! Professor Dave explains clearly so I can finally understand orthogonal

[Bruhhhhhhhhhhhhhhhhhhhhhh]

3:05 "four SQUARED plus two SQUARED plus negative one squared" lol im dying and good vid overall

[ddiverr]

clean, informative, and concise video, thanks guy

[bluefenix]

This explained it so well for me, you spoke clearly and didn't do messy sentences, and even paused after every sentence to process it 👏👏👏👏👏👏

[missghani]

can't thank you enough for this clear explaination

[banderallogmany]

3:52 I didn't get how the length becomes 1!

[apythonprogrammer]

This really helped me understand LLM model quantization just a tiny bit better

[JoseLopez-opsq]

A lot of good information in one short video; good overview.

[kidatheart]

I'm confused on the orthonormal part. There are 2 conditions for orthonormal vectors: (1) orthogonal; and (2) the length is 1. But the example on 2:56, the length is not 1 that negate the conditions of being an orthonormal. Can you please elaborate that part? Thanks

[mona]

Hello Professor and Thanks for your great explanations.
I was wondering why do not we have something called orthonormal matrices ??
and think orthogonal matrices are more like orthonormal ones!! :))

[ManojKumar-cjoj]

Inverse of orthogonal matrix = tranpose of matrix

[asifnahyankabir]

Amazing Professor! One day if God wills I'll come to meet you!

[deathworld]

Isn't orthagonality defined by having the dot product equal to null element in Euclidian space?

[aniketgupta]

Elaborate to some extent, I mean your beginning and laying down the foundation of the topic is good but should stretch it till good level.
Atleast that's what I feel missing in your videos, do please consider this if you see this comment.
By the way I love your videos from quantum numbers to biomolecules all are awesome.

[kryptoid]

sir, the inner product notation reminds me of bra-ket notation

[jds]

what happened to the visuals clarifications? its been primarily plug and chug for most of linear algebra..

[mcalkis]

Could someone elaborate on the weight functions? Is it just a correction factor so that a function can be orthogonal with respect to another?