[Linear Algebra] Linear Transformations

We discuss linear transformations in linear algebra.

#LinearAlgebra #Algebra #UniversityMath #Lecture

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We introduce linear transformations, which are essentially just functions. This is what linear algebra is about!

Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[_easymoneysniper_]

"A linear transformation is just multiplying a vector by a matrix". My teacher, in all his infinite wisdom and PhD's, tries so insanely hard to sound intelligent that there is no way he would explain this topic in such a simple, easy-to-understand way. This is the best explanation of this topic I have ever come across, both on the internet or in person.

[adamtisell]

You just linear transformed my grade

It would be so nice with a university without classes and replace it with Trevtutor

[juniorcyans]

I watched several series of linear algebra videos and this channel is the best! Concise and clear, no mathematicians’ nonsense at all!

[mwaleed]

No offense to Khan Academy, but here, Trev has taken the medal in explaining Linear Transformations.

[grhp]

Best video explaining this topic. You get right to the point and explain the material in a way that is easy to understand. Thank you!

[lemyul]

I used to not like this guy, but today his videos are finally making sense. My math skill definitely improved.

[truman]

What I've come to understand thus far in my college studies is that most courses have relatively easy algebra but is very focused on accepting and understanding the theory behind it. Without this knowledge the algebra becomes hard as you can't really understand what leads to the solutions you're looking at. Now, with linear algebra I have actually come to understand that the theory isn't really that complicated either - but it might take some time for it to click. For mathematicians explaining this is as hard as explaining to someone how to learn to ride a bike, it's so obvious to someone who has been doing it for long that it might actually be hard to remember what was hard with it to begin with. Because of this I think a lot of videos and teachers fail to make students understand the basics (atleast students like me, who are not by any means master minds). For some reason I got stuck on linear transformations, I have been trying to understand the basics to get to the algebra for atleast 10 hours frantically looking for help and stumbled upon this video. It took me half your video to have that "click" in my brain and suddenly it's all so clear to me.

I'm sorry for the novel but I really wanted to express my appreciation of your way of explaining this as basic as possible, you're helping out a great deal and having this sort of help online FOR FREE is a blessing.

Thank you a lot, and keep up the amazing work! (7 years late to the party)

[wihanuys]

Salman Khan has a worthy challenger for best mathematics teacher on the internet. This is getting me through 2020 without missing on education. Thanks a lot.

[ThePCxbox]

As someone who has been making games for years and using linear transformations in code that meant nothing to me before, that last example with the mirrored x axis blew my small brain away.

[legendaryxk]

I was so confused with the notation and couldnt understand sh&t i just knew it transforms but not how, Thank you for such simple explanation

[anshikamishra]

You are a great teacher.. you explain all the concepts in such a simple and easy way..Thank you so much for creating such good content.

[ethernet]

Just to clarify, 05:24, we DON’T have a free variable.

[dickyr]

If your A is a mXn matrix then (from 0:17 to 0:44) the vector x should belong to Rn (not Rm) and the vector b should belong to Rm (not Rn)

[hiddenman]

OMG this is siginficatly better explanation compared to my teacher.

[sumayyakamal]

best vid I came across about Linear Transformation, THANK YOU.

[SEE.ME.N.MRE]

I didn't get the part at 5:59 where it says: x1 = 3/2

[rasaqegunjobi]

That simple definition of Linear Transformation is awesome...

Great work 👆💪

[innocentkaziweni]

question
let pn be the space of polynomials of degree n or less in the variable t. suppose l is a linear transformation from po → p} such that l(1-4, l(t)-t3, and l(t2)-t-1. (a) find l(1+t+2t2). (b) find l(a +btct2) (c) find all values a, b, c such that l(a + bt + ct2) = 1 + 3t + 2t3

[ronnysanjaya]

Ya this are important understanding, not always n space thera are n vector might more or less.

[catcen]

this is a great video! Thank u a lot!
just one question; why x1 = 3+3x2; I thought it will be -3x1=3