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

Understanding alternate coordinate systems

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

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[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!!

[tricksend]

You have no idea how much this helps. I've been in an advanced linear algebra class for two months now and couldn't make heads or tails of anything until I started watching this. Thank you so much.

[jordanlevin]

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

[TinCarpter]

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

[HattManDoo]

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!

[cisco]

Omg, you math professors on YouTube 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 :')

[jingyiwang]

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

[TheGaIaxy]

Omg, I love love love you!!!! My bloody patronizing professor (who clearly has some sort of breathing difficulties as he always says "okay..." at the end of every sentence) took an hour TRYING to convey this concept to us and you did it in less than half of the time! God bless you! Know wonder America has 8 of 10 of the worlds top universities all of which is due to the quality of teaching.

[kevint]

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

[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!! :)

[nathanfernandez]

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

[sherrymao]

Thank you so so so much for this. This acts perfectly as complementary to my professor's lecture. You really make it easy and clear!

[EshwarNorthEast]

This is what I was looking for the whole day. 🖤🖤🖤

[soyluserdar]

Thank you so much for the lectures. They are simply amazing!

[TebiByyte]

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

[jonas]

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

[eggsforbacon]

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

[huynguyenanh]

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

[carsontibbels]

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

[diegofung]

I finally understand this concept ! Thanks