Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra.
Full series: http://3b1b.co/eola
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To any person who went to school in America. I was curious as to what age this subject is usually taught in your education system. I'm from New-Zealand and I think the standard here is to study this when one is 16-17 but I'm not sure. I ask because my brother and I have been in advanced mathematics classes for pretty much all of our time at school so far but I get the feeling our standards are behind other wealthy nations so I'm not sure how much that fact is really worth.
hey brown and folks please clear my doubt in this video. I haven't understood this transformation concept clearly 1. how really the i & j hat grid lines lands along with the transformed vector 2. how to compute function required to get the transformed vector
https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ This course from prof. gilbert strang is very intutional, and there is more mathematics. https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
Dear 3Blue1Brown, at 7:40 you said, "Then you can make highschoolers memorize this without showing them the crucial part that makes it feel intuitive." I feel your pain. So WHAT HAPPENED to math education that its so awful at times? I'm a senior Physics undergrad, and sometimes feel like my education and intellect has been intentionally sabotaged my whole life since I was in elementary school. What do you think are the causes? What are the factors?
In my country linear algebra is also taught in a disgusting way. But many students know to find and read a lot of good linear algebra books that are out there and also a lot of enlightening videos like this. Youtube and channels like this are really contributing to education.
I recently finished a basic course into linear algebra. I love how this video causes the material to actually become intuitive and make sense!
Looking forward to watching the other videos on this playlist :)
This is a good video thanks, but there is definitely a gap in the intuition at 7:45 which is how you get from the middle to the RHS geometrically. I don't understand why when transforming planes, a vector's x co-ordinate will move only according to the x co-ords of the transformed defining basis vectors i and j, multiplied by its's own x and y co ords... and likewise for the y co-ord. A visualisation of this would be really helpful!
I passed Linear Algebra at uni just by learning the algorithm to solve the questions, because I could not understand what a linear transformation actually was or what use I would ever have for it. Yeah, uni was bad. Great video, though!
Since I basically live in OpenSim (virtual reality) I find his explanations beautiful, but I kinda wish he would show some of this stuff in "real" terms of what the eye sees in a projection. I don't know how many times I have had to deal with people orienting their houses off the axis and then gone mad trying to put a picture on the wall. (I guess that would bring up the subject of object occlusion...)
We even deal with quaternions...
I am really really thankful to the people for making this video. I studied these thing at school to do excercise without knowing what it is and where it comes from. That was so meanningless. Now i understand its origin. It's wonderful.
It was a wonderful intuition of what does a linear transformation really represent !! Thank you so much for that!
I actually try to understand what a bilinear transformation represent. Can you help me for that ?
Great videos!! One remark... In the videos there is movement shown but in "reality" the transformation is only a start - end thing. I was wondering, would it be meaningful to express the orbit of such a "movement" by using functions of coordinates instead of numbers in the matrix? (given that the orbit is a function). For instance the orbit of the "shear" (8:31) can be written as [1 a; 0 1]*[x; y], with 0<a<1 and the resulting family of vectors is [x+ay; y]... just saying...
the best Explanation ever. could you please make a Video about Affine Transformation, about the 4by4 Matrix that encode Rotation, scale and translation together and what homogeneous coordinatesystem really ist. thank you in advance
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