Matrices, matrix multiplication and linear transformations | Linear algebra makes sense
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- Опубликовано: 19 июл 2018
- Brilliant.org: brilliant.org/LookingGlassUni...
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Matrices are often presented as a useful bookkeeping/ commutation tools to students- but there’s much more to them. When you understand what a Matrix really is so many parts of Linear Algebra will be completely obvious to you… including the formula for matrix multiplication and the fact that matrices don’t commute. So here's the big secret: A matrix is a linear transformation that eats a vectors and outputs another vector.
Homework questions:
Not all sized matrices can be multiplied together. Think about it in terms of them representing transformations from one space to another, and figure out which size matrices can be multiplied and explain why in the comments.
Consider a transformation that takes a 3d vector, and adds some fixed vector k to it. Say k is the vector 7 3 3. Is this a linear transformation or not? brilliant.org/practice/linear...
Imagine you have a matrix A that multiplies the first basis vector by 2, and the second basis vector by 6. How do you write A in this basis? brilliant.org/practice/linear...
Music: Epidemic sound, Summer nights 2
This video is an Introduction to Matrices but could be useful revision for school/university. If you have an exam, good luck!
8:59
I really appreciate these linear algebra videos. I took a class in the math last year in college and it was pretty aggravating, to say the least, that while everyone could explain to me how to solve matrix multiplication and even very elaborate proofs, NOBODY, not professor, TA, or tutor could explain to me what a matrix even was. To which point I was like, if you dont know what it even it is then how in the world could you ever apply this anywhere?
I really like the idea of matrix dimensions representing the dimensions of the input and output vectors/space. I feel dumb for never noticing that before.
OMG!!! I've been bumping my head against the wall thinking I would never understant linear algebra until I saw this videos. This is amazing!!! It is shocking to realize how many people manage to turn such neat and clear ideas into some awful algorithmic torture. Really, thanks a lot for this!!! By far this is the best youtube channel! Keep up the excelent work! ;)
I find it helpful to think of matrix notation like functions. g(f(x)) would say, do f(x) first then do g to the result, so ABv would be like A(B(v)) with the little nested brackets, "Do B to the vector first then A to the result". Then it's clearer they don't commute, the wording is just confusing.
I love how mathematically on point your video is. It communicates precisely what matrices are / what they are good for. I can’t comment on if this presentation is optimal for helping people understand the topic that didn’t understand it before. Probably it
You're not lazy, you're resourceful!
Amazing video the intuitive explanation was so well done
Your way of teaching and sense of humour is great!
Wonderful sense of humour!
Hello. Thank you for the videos.
I'm glad you are back
Wow such teaching, much learning
Yes, part two! And - as usual - you've done an excellent job explaining a concept that I doubt I'd ever be able to understand otherwise (although I'll have to wait until I'm home to do the examples since it won't work for me on mobile.) I agree with what you noted in this video around the 12 minute mark though; there isn't much point in knowing something without also understanding it. I was taught most of this stuff in high school about a decade ago and it just never stuck, yet here I am successfully learning how it actually works from a youtube channel... Thanks US educational system! :P
You're literally better than khan academy and 3blue(if you know who that is) combined! Please never stop making videos, they dont even need to be animated
>I don't understand why some courses insist on making linear algebra awful and algorithmic. What's the point of 'knowing' how to multiply matrices if you don't understand it.
You changed the way I look at math
I like the way you try to "teach" an intuitive approach.
I'm surprised that there are no row operations, haha!
I do have to say that AB != BA is not quite as obvious as you make it seem. Especially since we just talked about linear transformations whose definition involves doing transformations in different orders and getting the same thing. But of course many lin. alg. classes don't go into the intuition of why it's not associative, which is what you were presenting here. Speaking of intuition, I guess it really is true that all matrices are transformations - at least all that I can think of. I knew that they