Least squares examples | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

An example using the least squares solution to an unsolvable system

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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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[FoamySoaps]

This entire series got me through last semester. And if ever I need a refresher on something I come right back. Thank-you!

[aalhorani]

Great work. But I hoped that you focused more on the graphical meaning of this method.

Thanks

[DuderDudre]

@jakubnage lol abstract algebra is abstract.

Helpful video too

[ruhullahdaman]

only if there was more people like you!!!

[Zebban]

Thanks for doing these awesome videos. Thanks a million!

[Javlini]

Sal, you said in the previous video that the equation goes || b - ax^ || not || ax^-b || like you say here. The first one made more sense to me.

[jakubnage]

I would tend to disagree, linear algebra is quite hard and very abstract compared to the applications of calculus and where all the motivations for various ideas are explicitly mentioned when taught. Also, algebra II, III, abstract algebra, etc. are quite difficult and even more abstract.

[paulringab]

The only moment you think you're smarter than khan is when you know what 15^2 is :D

[DonVaillancourt]

So what does Khan talk about when he just chit-chats with people. He knows everything.

[reazshafqat]

my question would be: why are we multiplying A(transpose) rather than A(inverse)?

[nicksbologna]

Thank you soooo much I just did a math project on the Method of least squares and got a 100/100 on it because of your video

[theBIGamazingShim]

i forgot i had an assignment due tonight this video helped me finish in time =D thank you so much for putting this up to help!!

[FunOrange]

something tells me the solution that gives the least squares would be the centroid of that triangle

[burnfrais]

great stuff.
can you please do a video on splines, clamped and natural.

[saranshshah]

if i have 2nd degree equation like y=a+b*(x)+c*(x^2) and (x, y) are (1, 2)(2, 4)(3, 8)(4, 7)(5, 6)(6, 9)(7, 10) then what will be least square ??? find a, b, c.

[Toshinben]

Not enough to restore my faith in humanity, but still really nice!

[thepoet]

Very good! First I thought you said you were 10 years old. :P

Keep in mind that linear algebra is among the simplest college math. :)