Orthogonality and Orthonormality

Рет қаралды 189,735

Күн бұрын

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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Пікірлер: 73

@pkasb90 4 жыл бұрын

I must say your lecture supercedes those in higher institutions.

@STKeTcH 3 жыл бұрын

same

@miguelnuno928 3 жыл бұрын

Correct

@BoZhaoengineering 2 жыл бұрын

agreed.

@overl0ad816 Жыл бұрын

🤓

@julenekenyon3278 9 ай бұрын

I agree 💯. At this point you deserve my tuition!

@isxp 3 жыл бұрын

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.

@kartikkalia01 2 жыл бұрын

I'm at same situation as yours, please suggest similar videos/playlist.

@mohammedbastaki2101 3 ай бұрын

same here pal

@lingwaili1203 3 жыл бұрын

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

@tadabae 3 жыл бұрын

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

@beams9497 2 жыл бұрын

Haha saaaame

@macdonaldnnadi Жыл бұрын

15 minutes is crazy dawg

@missghani8646 3 жыл бұрын

can't thank you enough for this clear explaination

@ddiverr 4 жыл бұрын

clean, informative, and concise video, thanks guy

@Bruhhhhhhhhhhhhhhhhhhhhhh 2 жыл бұрын

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

@ayazohdy6221 5 жыл бұрын

Professor Dave explains 😂💕

@bluefenix1457 Ай бұрын

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 👏👏👏👏👏👏

@janakamohotti 2 жыл бұрын

Brilliant explanation!!! ❤️

@jainpravachan650 3 жыл бұрын

Thanks sir.... wonderful lecture

@jisaburo198 3 жыл бұрын

EXCELLENT videos! Thank you so much

@user-qv8mr8pe3i 2 жыл бұрын

thanks for awesome explanations!!!

@rodab3546 4 жыл бұрын

you explain so good

@raihansk5971 5 жыл бұрын

Amazing!!.........Explaination is awesome.....

@manishbhatia2724 3 жыл бұрын

Beautiful Explanation

@JoseLopez-op7sq Ай бұрын

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

@Dixxi91 2 жыл бұрын

Very good explanation, thank you

@user-so7gh7gd4v 2 ай бұрын

Amazing explanation

@Robert-gr1cl 3 ай бұрын

such good explanations, thanks

@mehuladhrit7883 3 жыл бұрын

Very nicely taught...

@apythonprogrammer7877 2 ай бұрын

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

@tknam3278 2 жыл бұрын

This is perfect!

@blakeelzinga1168 2 жыл бұрын

Thank you for this video

@adefisanadedotun797 Ай бұрын

Very understood Thank you

@mona5112 3 жыл бұрын

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!! :))

@suvarnamanojsingh 3 жыл бұрын

thanks that was helpful

@umehmoses8118 Жыл бұрын

I love the professor 😁

@asifnahyankabir7747 2 жыл бұрын

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

@colingillespie7635 3 жыл бұрын

The intro alone earns my like

@lamdawave 2 жыл бұрын

Good video. One question: If a square matrix has orthogonal column vectors. its inverse is not equal to its transpose. what should we call this type of matrices?

@mcalkis5771 2 жыл бұрын

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

@kidatheart4975 3 жыл бұрын

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

@criclal1787 3 жыл бұрын

Those vectors displayed at 2:56 are not orthonormal, we have converted them both to unit vectors and made them orthonormal thus.

@wealthy_concept1313 2 жыл бұрын

@@criclal1787 but if that's the case it means any vector can be converted to orthonormal at will ?

@MuffinsAPlenty Жыл бұрын

@@wealthy_concept1313 Any set of vectors can be "normalized" (meaning to make the lengths of all of the vectors 1). This does not, at all, change the angles between any of the vectors. The Gram-Schmidt Process (the next video in the playlist) shows us that any _linearly independent_ set of vectors can be made orthogonal without changing the span of the set. Taken together, given any basis, we can always find an orthonormal basis by first using the Gram-Schmidt process to make the basis orthogonal without changing its span, and then we can "normalize" the orthogonal set to make it orthonormal.

@deathworld5253 5 жыл бұрын

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

@yogsothoth2194 5 жыл бұрын

I think null just means nothing; or in mathematical terms 0 . So yeah you're probably right

@banderallogmany1912 3 жыл бұрын

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

@jds189 4 жыл бұрын

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

@srinityapadma5125 3 жыл бұрын

Thank you so much Sir.../\

@dgormley 2 жыл бұрын

Please teach at my university.

@ManojKumar-cj7oj 3 жыл бұрын

Inverse of orthogonal matrix = tranpose of matrix

@glennveniceaboy8876 3 жыл бұрын

your convention for magnitude of a vector is a bit confusing because the single bar on both sides is usually for absolute value, maybe you should've used double bars for it anyways, i learned a lot, thanks!

@carultch Жыл бұрын

Absolute value and magnitude of a vector have so much in common, they might as well use the same notation. I thought the double bars on both sides was completely unnecessary, when I was first introduced to the notation, after having become accustomed to just using the single pair of bars.

@desrepeerc206 2 жыл бұрын

3:23 Nice frankenbiting skills xD

@kaanylmaz1008 2 жыл бұрын

eyw reis

@prakashraj4519 3 жыл бұрын

video on caley hamilton

@kryptoid2568 3 жыл бұрын

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

@rushdisami5146 Жыл бұрын

Finally I understood Orthogonality.🤖

@anandailyasa2530 3 жыл бұрын

❤️❤️❤️❤️❤️

@marcosramirez2278 2 жыл бұрын

I found this channel because of flat earth videos, never did I guess this man would save my math grade

@user-iv4iy5rc1y 7 ай бұрын

TE DUA

@jaliyahkane5127 2 жыл бұрын

professor dave is an AI

@Gafa996Gaddisa 5 жыл бұрын

Is Ortho Greek word which means , straight up?

@georgesimos4914 5 жыл бұрын

"ορθό-ς" is used for other cases too; the one you say is one definition, but the one required for the concept of the video is "vertical"(an example is the mathematical expression "ορθή γωνία"="right angle")

@carultch Жыл бұрын

@@georgesimos4914 Even though I know that 3 out of 4 of the letters have completely different pronunciations, I instinctively read "ορθή" as "open". Even though I know it would sound more like "orthi".

@aniketgupta5750 3 жыл бұрын

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.