Vector spaces | Linear algebra episode 1

#vectors #linearalgebra

What does the word "linear" mean, in terms of both algebra and geometry? In this video, we explore the rules for vector spaces. Along the way, we will talk about music, chaos theory, apples and oranges, quantum physics, and more.

Here you can find the music you heard in the video:   / geert-van-damme-289809712  

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[3B1B 1]    • Essence of linear algebra  
The essence of linear algebra. The de facto starting point if you want to learn more.

[MTB1]    • Part 1 Linear Algebra: An In-Depth In...  
Math the Beautiful. Detailed, very well explained. A great resource for beginners. Heavy focus on geometry rather than specific coordinates.

[SUDG1]    • Why do we care about vectors?  From Z...  
Over time, this is going to turn into a great reference on geometric algebra. But the introductory videos already give a very detailed account of how vector spaces work. The explanation is easy to follow, and starts from absolute zero.

[VIS1]    • What is...a vector space?  
The abstract definition of a vector space, followed by many concrete examples such as arrows, polynomials, and matrices.

[BRIGHT1]    • Linear Algebra 1 | Introduction  
This is a more formal and advanced introduction to vector spaces. Good if you already have a background.

[CTC1]    • Human Beings Can Solve THIS Better Th...  
Solving a sudoku by counting degrees of freedom.

0:00 Introduction
1:31 What does "linear" mean?
4:32 Non-linear systems
5:36 Applications (physics, AI, music)
8:51 The rules of vector algebra
11:50 Quantum superposition
14:00 Arrows are geometric vectors
15:48 How to subtract vectors
17:37 Linear combinations & spans
20:40 Degrees of freedom & constraints
23:08 Basis vectors
29:00 Coordinates are basis-dependent
32:54 The map of linear algebra

This video is published under a CC Attribution license
( https://creativecommons.org/licenses/... )