Linear Algebra - Matrix Transformations

Matrix multiplication and linear algebra explained with 3D animations.

[EugeneKhutoryansky]

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[Tiago]

If I had these videos available since my childhood, I would never ever thought I am stupid with math. These explanations were exactly what I missed.

[RangaNanayakkara]

Man with people like you we can start by teaching calculus to primary students. Great Work !

[EugeneKhutoryansky]

I just created a Patreon account and added the link to my YouTube home page. Also, in case, you have not already seen them, I uploaded several other videos recently. As always, for each video that you like, you can help more people find it in their YouTube search engine by clicking the like button, and writing a comment. Lots more videos are coming very soon. Thanks.

[napomokoetle]

You must be the best teacher I've ever encountered! You must be God sent... Thank you!

[malmarb]

where was this channel when i was in school 😭 . i used to solve these equations without even understanding them, i just learn the rules and how to multiply them and went to the exams, but the visua representation makes it so easy to understand .
I was taught to do it like this but i didn't know why should i do it like this, but now i know why

[starwarsjk]

Your channel is 100 times better than Khan Academy! You actually explain Matrix transformations and one way they can be derived. Channels like Khan Academy spoon feed you information like multiply this number by that number and this number by that number. They don't tell you why you should do that.
Your video on Linear Algebra demonstrates WHY we multiply matrices by vectors in a certain way. Before I saw this I thought Matrices were something weird we just made up that did not behave like normal mathematics. After watching this I realise that matrices are truly a part of mathematics and they are made to solve real mathematical problems, not made up as some weird form of arithmetic.
If all of youtube was deleted and I could only choose to save one channel, yours would be the one I keep. Good JOB!

[ArpanD]

What I love about this channel is its unique and diverse content. Like 3Blue1Brown focuses only on math, but in Professor Khutoryansky's channel you will get physics, math, philosophy, engineering etc.., all visualized in an epic manner. This channel is a revolution, it really is!

[benjaminasmad]

Great!! During my college days, I had a hard time of understanding the concepts of matrices and vector space, now, you make it simpler and understandable! Thank you so much!

[slavakotelnikov]

Eugene, what a fabulous explanation. I have been struggling (with no luck) for about 2 months to understand how the transformation matrix is built, but then I saw your video and it all became crystal clear to me. Please continue with matrix algebra, you definitely have got the right talent to do teaching!

[EugeneKhutoryansky]

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link:
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[mypoostank]

Your videos are so helpful! Why doesn't my teacher just show us your videos!! A confusing week's worth of class was simplified in this 20 minute video. The creator of this is a genius and should be recognized more! Thanks for these awesome videos!

[SinanAkkoyun]

For everybody struggling with why rotations are not linear but still are a linear transformation:
You do not rotate a vector on a fundamental level. With a rotation matrix, you describe a non-linear function (sin/cos) OUTSIDE the transformation. The actual _linear_ transformation is linear. You compute the amount of linear cominations required for something that acts like a rotation in advance, the act itself _is still linear_

What I am saying is, that when you apply a rotation matrix (e.g. 30° around x axis) to a vector, it snaps the vector to the 30° position. IT DOES NOT ROTATE inbetween when only applying one 30° rotation matrix once!
A vector can make any sorts of non-linear movements, but these are just non-linear because you compute the matrix for each step outside with non-linear inputs





(This is just a complementary explanation, the video is right in every way and is awesome!)

[ericosmostech]

Everytime I watch these videos, my jaw drops with Wonder & Enthusiasm... Incredibly amazing this channel is! ♥

[metcas]

To be quite honest, I was initially taken aback when I stumbled upon your channel and its content. It was a little strange at first (the animation, primarily, ) but I've come to really, really enjoy your videos. Thank you very much for the extra clarification on many subjects. It really helps fill in the blanks for me. It is in such straight forward manner as well. Bravo.

[dhavaldeshmukh]

Its the greatest channel that has everything. Physics, electronics, maths

[tarikbadi]

This is the best video I have ever seen on youtube.

[fortoday]

Can you make a video about eigen values and vectors please? I need an in depth understanding.

Maybe, matrix rank, vector spaces, etc.

Linear algebra is really interesting!

[bradleycollings]

Such a fantastic resource as always! Thank you and may more people find your channel.

[Alexandre]

My favorite teacher!!! You made me enjoy the Universe in a very unique way. Thank you!