This felt like the incoherent, quick and unplanned ramblings of a schizophrenic, and i don't think i've ever had such a great math lesson.

😂😂some mad man comes from the mountain and says let's double the input functions. Awesome video

I have never seen someone with such pure passion for mathematics!
Never stop bro, you will surely be a part of history of mathematics.

What you’re doing is special. Of course you still are gonna get much better at making these videos. But the idea of teaching something and making it fun at the same time is v impressive. I wonder how videos will be a year from now. You Got a new sub

y = ax + b is very close to linear. It's what we call affine. All the equations need to pass through the origin. And also, z = ax + by is good to, even though it's not a line; but a plane. I like to think about it like you have a box full of lego bricks with some number of different bricks, that stack in various different directions. Linearity just means you're only allowed to stack bricks from the box you're in, one ontop of the other, but you can stack as many ad you want ontop of eachother e.g. if you have bricks x and y, you can stack xs on eachother by adding them consecutively, and you can stack ys ontop of eachother by adding them consecutively, and it doesn't matter what bricks you start with, or in what order you stack them, you get to the same spot with the same bricks ax + by.

Man, I didn't know I really need this channel. I'm currently studying Biomedical Engineering and have been (and still am) struggling with theoretical maths, even though I managed to pass those exams, albeit with mediocre results since I can't spend too much time on one subject. It's such a breath of fresh air and truly inspiring for me to see a vlogger that focuses more on teaching things and making it fun, which we all are in dire need for more of this. Keep up the great work buddy!

It’s about 50 years since I learnt and used  matrices in my mathematics degree at college.  Never had to use them in my work. Forgot about them. But somehow I find this interesting.  Great vid.  Keep em coming.

Bro I thought "15 minutes of listening to something I probably won't understand", and nah it went by fast and I got it. Thanks!

I love your philosophy and passion for math! Super inspiring for me as a hs student :) It is a whole new mindset when you study math for fun vs. to pass an exam/class.

You explain just like how i think so this is EXTREMELY helpful

I like your explanations, you can tell that youre not mired down with scholastic jargon and overcomplicating stuff. Also, i like youre elemental approach where you build up the picture of what youre explaining. Im also a lifelong autodidact and taught myself advanced engineering mathematics and gained my degree eventually without attending a single class!

Subscribed! Keep these coming. Oh and thanks for the indirect book recommendation 😉 i love these forst editions, they have a different depth to them! 👍🏻

"one number goes in, one number comes out. Bob is your uncle" - This was legendary😂😂😂

Being a computer science graduate, i have had issues with math and programming so i took it up as a challenge to learn the math needed for computer science ( machine learning to be specific). I am almost true with college algebra and going into calculus next. It’s has been “🤔😀😄😱😨😰😶😬😄 in repeat”so far but it’s worth it. Everything starts to make sense and that’s where the beauty of maths shows. Keep up the good work. Who knows!? The world might need your knowledge one day 💯👍🏾

Love your style of videos. THANK YOU THANK YOU THANK YOU for making matrixes actually make sense😭😭. It was unironically so confusing and no one actually told us what they were, we just started doing them. This video has been extremely valuable, wonderful job and I hope you succeed in your mathematical journey.

How this channel  has no more vies! I see my self in you when you are explaining, it's as if words fall short, (since your 3blue1brown recommendation I liked you) I'm studying architecture, but my fundamental idea to grow on it is have a solid mathematics base; the more I learn about it's beauty it becomes... hard?,  world is complex & easy at the same time, I just don't understand how your video apeare in this moment of my life...

So a guy just said "why can't we have multiple outputs? It's kind of a waste..." And we got matrices

I just found your videos today, and they're amazing! I love how simply you explain concepts and your mini history lessons.

I don't really know so much about matrices, but I do know the history of how vectors developed. Originally, Hamilton wanted to use the complex numbers to describe 3 dimensional space, but because they were 2 dimensional, he had to generalise what he had into 3 dimensions, but he was running into a wall. Hamilton had a big insight to use a 4 dimensional generalisation of complex numbers called quarternions, which had a scalar part (a number) and a vector part (ai + bj + ck). Taking the product of quaternions gives another quaternion with a scalar part, which you can find by taking the modern scalar or dot product, and a vector part, which you can find by taking our modern vector or cross product. This was great, but they found the behaviour of quaternions to be unwieldy for more simple applications (Oliver Heaviside and others were trying to use them to describe Maxwell's equations), so Heaviside and others developed modern vector analysis, which has vectors and a series of predefined behaviours with products that are taken from quaternions, but without the behaviour of SU(4) (multiplication encoding rotations).

I feel that matrices are best understood as transformations of vectors. Dgmw, systems of equations is great and all, but I just feel like transformations are more powerful, in part because you can get to systems of equations through transformations, but also as soon as you can really see and prove that matrices are basically a list of vectors, and those vectors tell you how they transform the standard unit basis, that insight really just opens up the field to all the crazy stuff like eigenvectors, diagonalisation, spectral theorem, etc.

Love this man. The rest of the comments agree on that too — you’re def gonna grow like crazy if you keep this up. I wanna try do this kinda thing someday maybe too

Thank you for the video. I knew about matrices but I didn't know anything about its history and how it evolved. Now I think I have a much clearer understanding of what matrices actually are