This is the full first lecture of a course on Linear Algebra. Given by N J Wildberger of the School of Mathematics and Statistics at UNSW, the course gives a more geometric and natural approach to this important subject, with lots of interesting applications. Our orientation is that Linear Algebra is really “Linear Algebraic Geometry”: so teaching the algebra without the geometry is depriving the student of the heart of the subject.

The first lecture discusses the affine grid plane and introduces vectors, along with the number one problem of linear algebra: how to invert a linear change of coordinates!

Intended audience: first year college or undergraduate students, motivated high school students, high school teachers, general public interested in mathematics. Enjoy!

CONTENT SUMMARY: pg 1: @00:10 N. J. Wildberger Webpages:

web.maths.unsw.edu.au/~norman/index.html

pg 2: @02:10 Linear Algebra to Linear Algebraic Geometry; example; applications

pg 3: @04:52 2-dim affine geometry (no notion of perpendicularity); affine grid plane; the core problem of linear algebra

pg 4: @09:27 no distance measurement, no special point (origin), no angle

measurement; relative positions can be described; affine grid plane; vector;

connection between algebra and geometry

pg 5: @13:52 refinement of the affine grid plane; rational number

pg 6: @17:34 Multiples of a vector; adding vectors; basis vectors e1 and e2

pg 7: @22:34 Two affine grids and 2 sets of basis vectors

pg 8: @27:13 change of basis vectors example

pg 9: @30:47 change of basis example continued; Main Problem of Linear Algebra (MPLA)

pg 10: @34:03 summary of previous example; (MPLA) General case in 1dim; (MPLA) General case in 2dim

pg 11: @40:32 questions; Exercise 1.1

pg 12: @41:42 Exercises 1.2-4. (THANKS to EmptySpaceEnterprise)

Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of each lecture. Great for review, study and summary.

Please consider supporting this Channel bringing you high quality mathematics lectures by becoming a Patron at https://www.patreon.com/njwildberger?

A screenshot PDF which includes WildLinAlg1 to 26 can be found at my WildEgg website here: http://www.wildegg.com/store/p107/product-screenshot-Wild-Linear-Algebra-A-pdf

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/

Screenshot PDFs help you navigate through most of Norman’s video series: they can be found at http://www.wildegg.com/wildegg-store….

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/…. I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?… .