Applications of the dot product to planar geometry I | Wild Linear Algebra A | NJ Wildberger

The dot product, or inner product, is the main source of metrical structure for planar Euclidean geometry when we work in the framework of linear algebra. In this video we show how it leads to the idea of a linear functional, how it gives us a direct and geometrical understanding of lines via normal vectors, and how to work with projections.

************************

Here are the Insights into Mathematics Playlists:

Here are the Wild Egg Maths Playlists (some available only to Members!)

************************

[TheLetterW]

Excellent video.  Interesting take on projections.  Found it much more symmetrically appealing.

[pickeyberry]

Video Content

00:00 Introduction
01:57 Linear functionals
10:54 A linear functional can be thought of as a linear transformation of a relatively simpler kind
15:50 Lines in the plane
18:53 Projections
29:23 General projection formula

[davidkeirsey]

Excellent.  Applications to PT symmetric lattice systems.