Vector transformations | Matrix transformations | Linear Algebra | Khan Academy

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Introduction to the notion of vector transformations

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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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Sal, you're my function to success.

InsaneBastardGuy
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Thanks a lot!! Knowing that a ''Transformation'' is just a fancy way to call a especial kind of functions makes so much easy the understanding of Linear Algebra texts...

jazerazo
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3:13 ... Whats that pokemon? It’s Ditto!! 😊

Frappuccino
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Sal, i always learn something when I watch you guys

fevenjoshuacarpe
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Aight, my journey to become accelerator starts here

walktroughman
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Thanks Thanks, helps me a lot more than in the school and on the book.

desxse
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you just mapped a complex subject into something everyone can understand ;) sweet

jishuenkam
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Holy freakin' crap!

Thank you! It all makes sense now. The "Transformation" has been throwing me off so much in Linear Algebra.

DillonRedding
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I came here because of anime character (Accelerator from A certain Magical index or Scientific Railgun)

aljoneldimaguila
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Amazing. Thank you for all you do, Sal!

amandafalke
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Around 5:38 he gives an example where he defines the codomain as a "subset of Rm". Wouldn't this just be the overall set of Rm? Since the range is the subset that actually gets mapped to, wouldn't any value be in the full set of Rm?

CabCallawayMusic
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You did it again. Beautiful explanation. Thank you God Khan!

christianwireko
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I came here to get my Masters in electronic and electrical engineering.

dorky
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Thank you for posting this amazing video!!

suzuyure
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Could you make a video on the rodriguez transformation?

NXTstorms
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Sorry if im wrong or if its to obvious, at 13:17 did you mean ... plus 2x2 when you wrote 2x1?

planthax
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Not too convinced! Does this topic relate with linear transformation in maths ??

jonathanidam
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@dunrunan Yep, I've yet to find a good linear Algebra text book...

fuckooo
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Hey Sal, at 13:15, you wrote that the transformation equaled (x1+2*x1, 3*x3) when I think you meant (x1+2*x2+3*x3)

Flopsaurus
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hey does anyone know what drawing program he is using?

cortek