Linear Algebra: Projections

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In this video, we discuss the idea of projection and the notion of decomposing a vector which is one of the most important concepts in linear algebra. We also do several proof based examples.

00:00 - Introduction
00:19 - The concept of a projection and the decomposition of a vector
08:22 - The formula for projection
11:19 - Example 1
16:38 - Example 2
21:51 - Example 3
25:29 - Example 4
29:06 - Example 5
32:34 - Example 6
39:37 - Example 7
  1. Math for Thought
  2. Linear algebra
  3. Norm
  4. Basis
  5. Transformations
  6. Eigenvectors
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Комментарии
Автор

Who thought it would be a good idea to use u and v as variables.

howitbe
Автор

cloudy, awesome work bro. is it safe to say when a vector is a scalar multiple (parallel), that we are projecting SCALED UP OR SCALED DOWN versions of this vector? might be a silly question haha... and also, when a variable is parallel, does that mean the variable is projected onto an arbitrary position vector? For instance, you said vector x is parallel and a is a vector, that means its proj_ux? Just clarifying!

jasonmantri
Автор

would it be clever to say that the projection formula is the scalar multiple of the parallel vector "u", since the dot product portion represents a bunch of scalars and the u part that is the vector part is a vector in the specific span with a bunch of linear combos. In other words, when we project a vector, we're looking at a "scaled" vector? enlighten me upon that pls haha

jasonmantri