Coordinates with respect to a basis | Linear Algebra | Khan Academy

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Understanding alternate coordinate systems
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In 45 seconds of watching this, I learned more than my entire hour and 15 minute long lecture.

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Most teachers just want to complete their hours.

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How exactly did you learn something in 45 seconds? He didn't even explain anything in the first 45 seconds. Just what kind of professor did you have?

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I'm crying of happiness right now because I finally understand what bothered me since last week!

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I just have to say that these videos bring a level of understanding to my classes beyond anything that a book or my professor could provide me. Thanks so much for the video!

[@kevint6878]

Amazing video! Love how it shows how the coordinate system that we've taken for granted works!

[@EddieVanWilder]

15:44 you say this is almost trivially simple or obvious but its only because you have boiled the concept down to the fundamentals in a beautiful way. Thank you!!

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I have been puzzled with this point for a really long time. Now I finally understand! Thank you so much for this video!

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I found this to be incredibly helpful! Now I can sleep at night without this bothering me. Lol

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[@huynguyenanh8984]

Thank you so much, it's difficult to wrap my head around this concept and you nailed it perfectly!

[@coolmisskitkat]

I couldn't find out what they meant by coordinate vectors anywhere. There are only definitions and how to find it. But no where did it specifically lay out what we were doing. You're awesome, and please keep it going! Math should be understood not just mechanically done, as you show in your videos!

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Anybody still watching in 2019-2021?

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Jan 15, 2020

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March 5, 2020 :)

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April 1, 2020

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Jan 31, 2021

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I finally understand this concept ! Thanks

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Omg, you math professors on KZbin should get together and form a new university.. you'd produce a bunch of math geniuses. (Me among them!!) Thank you so much!! You give the much needed quality to my college degree :')

[@nathanfernandez8952]

phenomenal explanation of coordinate vectors. I literally gasped when you drew the skewed graph of v1 and v2

[@OttovonSchweinichen]

Maaaan, during these 34 minutes of videos (I have watched another one about change basis matrix) I have learned more than during whole semester, thank you!

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Woahhh that was so awesome how it just pieced together...

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This video has helped soo much. Finally I understand what is going on.

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You make so much more sense than my professor. Thank you soooo much.

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This man is single handedly carrying my Calculus and Linear Algebra Uni courses

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Man you are grrrreat. Amazing explanation, with the visuals as well. My brain is thankful

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Thank you so much. Easy to understand.

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I didnt find this on spanish. Thank god khan academy has all this lesson

[@michelledotx]

thank you for this explanation and making sure we understand where the coordinate vector comes from! this really helped me after i didn't know what was going on in my lecture and i was scared that i would start falling behind especially with a quiz coming up. thank you!! :)

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Amazing Explanation!

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13 years in and this is still a really good explanation

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That was super cool!

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This same guy has been teaching me math since 5th grade, and still does a better job than most of my teachers.

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Thank you, 15 min well spent viewing your video. Wish my teacher would stop reading off the book and explain the materials like u just did.

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Verry helpfull.

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The greatest math teacher I have met.

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i love watching the views increase right before my exam. Good luck guys.

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how did you do it can you share with me , thank you

[@user-bu8mg7uq3s]

thank you

[@nenzattibellece4459]

This was great, thank you. Now, why do they throw the ortogonal coordinate system at us in the middle school as if it was the only coordinate system and having nothing to do with vectors? It gets so stuck in the students mind that it becomes almost impossible to accept this "new" reality, the truth. Thank you, again.

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[@SV-zi9os]

what a geometric representation!!!!!1

[@paulinaaa2011]

Blew my fuckin mind yo

[@kundan_28]

Where do the 3 and 2 come from??

[@stanleylim4458]

It's just a random example. e.g for example I have a vector 3(v1) + 2(v2)......an example of a coordinate vector with respect to the basis.

[@xuruoying7682]

Oh. Kernel trick

[@bmanman84]

so coordinates are the scalars?

[@MrVishyG]

lol trust me, I'm in one of the top American universities, and it's still a nightmare to listen to most professors

[@Ma7m9d]

At the start, how come you say V belongs to Rn, and then the basis B in V is k-dimensional? shouldn't it be n-dimensional as well?

[@olumidevic6230]

For basis, dimension has a different definition. It is the number of vectors in the basis. I know its confusing, but that's how algebra is.

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[@maldinnisanchez8010]

I See i of these people wonderful people learned this math. i am still find it hard. i am not saying the teacher is wrong. it is just i am finding it really difficult to learn it and i have been trying for 2 years now. i really need help. can someone help me? really need it we can work out a deal.

[@Javlini]

+Maldinni Sanchez Make sure you define the words you don't understand mate. It's more important than you might think.

[@DhwanilDesai1212]

can u tell me how 2,1 and 1,2 matrix convert into 1,0 and 0,1 plz asap reply