The Gram-Schmidt Process

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We know about orthogonal vectors, and we know how to generate an orthonormal basis for a vector space given some orthogonal basis. But how do we generate an orthogonal or orthonormal basis given some other basis comprised of vectors that are not orthogonal? We can use the Gram-Schmidt Process! It looks tricky at first glance, but it's not too bad. Let's give it a try!

Script by Howard Whittle

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This 10 minute explanation is better than 2 hour lecture in class.

omyrazeem
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Saw you destroy flat earthers earlier in the year and now when I’m taking linear algebra in university, you come through for me again. Great vid!!

brownviking
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Looked through several videos describing Gram-Schmidt and this was the most clear, thank you!

jessicapeng
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Wow. I love it.


It's easy to get mixed up when you're using it, so it's great so see this explained in simple steps.

maxxie
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I really, appreciate your way of presentation ( short, precise and to the point). I never understand my lectures without you. Thanks a lot professor Dave.

bioscience
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Simplicity is a great demonstration of genius. Thank you!

abnerandreymartinezzamudio
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Thanks, looked several videos on this but your explanation is the simplest.❤

swaroopsalvi
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your videos are saving me hours of studying time for my upcoming Linear Algebra exams 😭 thank you

Atlas_Enderium
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Best explanation I saw on YouTube. Keep uploading such useful content. Thank You.

AkhtarMehraj
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Best, easiest & most visual explanation of the Gram-Schmidt Process. Thank you Professor Dave :)

YTjugal
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It's 11 pm. I have my final exam in linear algebra tomorrow and have not had time to learn this process yet

norawallberg
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Prof. Dave is a genius in education. We NEED you!

braydenchan
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I loved how the explanation is so simple and clear, thank you professor :)

BlackCat-ovtc
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I am watching your video's related to linear algebrs in nov. 2024 this is so helpfull for me..❤😊
From India 🇮🇳 (University of Delhi) in 1st year

vardan_kashyap
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I really have to thank you. I discovered your channel in my junior year when I went abroad to the US and studied Physics 1, when I already studied Physics 3 in Italy, my homeland. Obviously, your videos were very basic because the content was such. I'm now in my freshman year in university, and have rediscovered your channel through these videos about linear algebra and calculus BC, and am really glad I did, you have helped me a lot. My partial went amazing, all exercises were flawless (although I have to study theorems better), and it's also thanks to you :)

NicolaMigone-ff
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understood 2 days worth of lecture in 2 minutes due to this video

dhirdeepakmichael
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Very simple and helpful explanation Thank you Sir 🙏🏻🙏🏻

yogitajindal
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Terse and concise explanation! Thank you

vaibhavkhobragade
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Sir you are very understanding. Keep it up.

bhattialdo
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bro in just one day I finished more than 20 hours lecture just by using your videos. thank alot man you saved me ❤

kasra-irio