Visualize Different Matrices part2 | SEE Matrix, Chapter 1 скачать в хорошем качестве

Visualize Different Matrices part2 | SEE Matrix, Chapter 1

Visualizing, identity matrix, scalar matrix, reflection matrix, diagonal matrix, zero matrix, shear matrix, orthogonal matrix, projection matrix, inverse of a matrix. Chapters: 0:00 Shear Matrix 1:57 Orthogonal Matrix 5:20 Projection Matrix 7:30 Inverse 9:35 What exactly is a Matrix ? Hopefully providing more intuition about matrix transformation on vectors and making the very abstract object of matrix, more relatable to us. This visual approach to matrix transformation also is the foundation to the Grand Finale of visualizing SVD. This video wouldn’t be possible without the inspiration of the legendary 3b1b :    / 3blue1brown   and the animation software - Manim, which he wrote:    / 3blue1brown   and the Manim Community: https://docs.manim.community/en/stabl... Video Sins: 1. It’s clear we have 4 different ways of shear transformation in 2D. But in 3D, are there 6 different ways ? Or are there infinite number of ways ? When I tried to look up the exact definition of shear transformation in 3D, I actually couldn’t find a very rigorous definition. Base on this definition: https://www.cut-the-knot.org/WhatIs/W..., it seems like there should be more than 6 different ways. I feel like shear transformation is one of those things that doesn’t actually doesn’t need a formal definition, it’s not like symmetric or orthogonal or identity matrix, which serves significance in other proofs of linear algebra. I could be wrong tho. 2. 3:38. “Orthogonal matrix always produces a rotational transformation to some degree” (firstly, pun intended). But here is the war on definition again. What exactly is a rotation ? The main debate is if the definition of rotation should also generalize improper rotation https://en.wikipedia.org/wiki/Imprope..., which happens when the determinant of the orthogonal matrix is -1. To be honest, I have no idea. Perhaps the better way I should phrased it was “a rotation transformation can always be described an orthogonal matrix” rather the other way around. Image Credits: Mugen (samurai champloo), Spike (cowboy bebop), Dandy (space dandy), Obito (naruto), John Green, Gilber Strang, Eren (attack on titan) Music Credits to Nujabes, may he rest in beats: 1. beat laments the world 2. aruarian dance 3. flowers 4. modal soul Other Music: 1. Going Down by Jake Chudnow 2. *MACINTOSH PLUS - リサフランク420 / 現代のコンピュー* My Email: [email protected] Feel free to send me suggestion for future video ideas.