The Gram-Schmidt process | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

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Finding an orthonormal basis for a subspace using the Gram-Schmidt Process

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For me, 20 minutes of this is worth more than a 2 hour lecture. Thank you!

baekalfen
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Khan Academy coming in clutch right before my Linear Algebra final #KhanAcademyIsBetterThanNYU

asiasuarez
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Although my linear algebra instructor made this easy to follow in terms of the steps and calculations, watching this video I know actually understand WHAT we are doing when we perform these steps. Thank you Sal for the great video tutorial.

greensasque
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i've never understood this quite right at college but now as i take only this one 20 minute lecture at khanacademy i understand everything. thank you!!

knjiga
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Saving mathematic lives out here, thanks fam

steveosazuwa
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This felt so intuitive... my mind is blown. Thank you for showing us why math is so cool!

JT-hlzd
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A day before my optional resit of quantum mechanics and here Khan Academy is, saving the day again.

seonaxus
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Thank you so much, i am so grateful to you Sal. You literally changed everything....

derek
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Hes definitely right when he said its not that bad when youre dealing with the numbers. Memorize the equations and its not too bad. Understanding the proof and why is the hard part.

theoldblood
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1:28 How to ensure a basis is orthonormal.
5:55 Replace v2 with the orthogonal projection of v2 onto v1 and the vector component of u orthogonal to v1.

lynny
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I don't have words to show how grateful I feel now

anweshadutta
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Man this guy's the best. Been using these vids since middle school, and I'm in grad school now. Thanks Khan Academy

Space_Lion
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thank you khan academy, it was really useful .i was struggling to understand hilbert space now you made it easy.

akashraj
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It became clear later on in the video. thank you so much for making it free!

ruttananrongsawad
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damn your U :p
Tutorials are really nice, and that's really helping. Thank you :)

InnoRative
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great sir!! i love listening to your way of explaining things

rishubits
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This is so well explained. I had to go back watch it twice though. But makes complete sense now. Thank you so much!!!!

ellen
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That awkward moment when you understand something in maths :') Thanksss!!

noneofurbusns
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minor correction @2:15 he should've written " || u_1 || " instead of just " u_1 "

nrrgrdn
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I can't believe it, I'm starting to love Linear Algebra

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