Geometry with linear algebra | Wild Linear Algebra A 27 | NJ Wildberger

This is the first video of Part II of this course on linear algebra, and we give a brief overview of the applications which we will be concentrating on.

The first topic will be the connections between linear algebra and Euclidean and other geometries. Linear algebra provides an excellent framework for geometry, allowing Euclid's axiomatic approach to be replaced by logically more solid definitions and proofs. However for this to work seamlessly, a more algebraic approach than found in most texts will be here adopted. We will use ideas from Rational Trigonometry, and the dot product (or inner product) will play a central role.

We motivate these developments by going back to Euclid's understanding of mathematic's most important theorem: Pythagoras' theorem, and the intimate connection with the notion of perpendicularity.

Video Chapters:
00:00 Introduction
1:06 Linear algebra: the greatest 20th century contribution to pure mathematics
2:21 The language of linear algebra in operator algebras, representation theory, harmonic analysis, geometry, algebra, algebraic geometry
3:24 Problems with foundations of Euclidean geometry
5:57 Basic affine geometry
10:29 Euclidean geometry = affine geometry + "metrical structure"
13:56 Back to Pythagoras!! (via Euclid)
22:57 Perpendicularity

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[Myrslokstok]

Interesting should have had this course before I past my course.

[robkim]

1 a wonderful course   ....want to write  a paper in