Linear transformations | Matrix transformations | Linear Algebra | Khan Academy

Introduction to linear 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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[HoRiz]

4 people linearly transformed them selves from college students to college dropouts

[jamesnganga]

Its awesome how you break down everything in Linear Algebra into  understandable modules. When my lecturer teaches, everything is like encoded in alien codes but wen i come here.... i kinda understand it all. Big up Sir. You are my tutor.
*from KENYA*

[canadianthroneholder]

of all math courses at university linear algebra involves the most memorizing and least understanding of why formulas work the way they do. I much prefer calculus and stats where formulas make more sense and thanks for helping out with linear algebra your videos are good

[fashionofthechrist]

I could just watch MIT Open Courseware and you all day, buy all the textbooks and I wouldn't need university. I could be educated as an engineer from YouTube and readings alone. That's remarkable.

[arrowheadspring]

These videos are better than a lot of Linear Algebra courses at universities.

[monkeyska]

After hours and hours of reading my textbook and looking at other youtube videos, this has been BY FAR the best explanation of/how to apply a linear transformation!

[TakingChances]

Thanks for doing what you're doing Sal! :) This video was posted 9 years ago and it's awesome seeing how many people you've helped. You are going to save my grades for a midterm tomorrow haha.

[Serpentombre]

You speak a language anyone can understand, this is just perfect!

[yourallstar]

"What is our... Let me do a color I haven't used in a long timeWHITE!" 8:19

[TinCarpter]

20 minutes here worth more then any number of hours in a lecture hall.

[ninosawbrzostowiecki]

I'm also obsessed with linear independence.  

[SW]

Learned more from Sals linear algebra videos than I did in college

Your videos are a great help in studying for my upcoming exam. Thank you very much for explaining the concepts so clearly.

[ryanshields]

Big ups to da man making these bad boys, bloke is absolutely carrying me rn

[yuxrazafar]

i have been strugling with this concept since my college lecture, but this man cleared it all... very well explained

[arranstobbs]

iv been studying for an exam, this has helped loads!

[bakhodirjonkakhkharov]

1.3 mln views and just 5.6k likes? People are so ungrateful. They watch these amazing tutorials for free and don`t even press the like button((

[lyricjam]

the explanation is so clear that i could understood it in english (my native language is spanish).
good job.

[dontbothermeimjust]

I finished my engineering graduation without ever understanding linear transformation because I don't get its meaning in real life. I am sorry but this did not help either. I know how to do the math, I just don't know what it means.

[suyashneelambugg]

@Khan Academy - So the example to demonstrate where the linear transformation is not valid is one where we did a non linear operation on the variables. So this way, i should assume ...L.T. to be valid in most cases where there is an absence of any explicit non-linear operation on the variables. ?