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source: njwildberger 2011年3月7日

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.

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

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?... .

1: Introduction to Linear Algebra (N J Wildberger) 43:31 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!

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)

2: Geometry with vectors 44:15

3: Center of mass and barycentric coordinates 48:11

4: Area and volume 56:03

6: Applications of 2x2 matrices 43:47

5: Change of coordinates and determinants 48:36

7: More applications of 2x2 matrices 55:13

8: Inverting 3x3 matrices 45:44

9: Three dimensional affine geometry 43:02

10: Equations of lines and planes in 3D 1:08:52

11: Applications of 3x3 matrices 53:36

12: Generalized dilations and eigenvalues 55:35

13: Solving a system of linear equations 49:13

14: More row reduction with parameters 49:13

15: Applications of row reduction (Gaussian elimination) I 41:38

16: Applications of row reduction II 57:14

17: Rank and Nullity of a Linear Transformation 1:01:09

18: The geometry of a system of linear equations 1:08:59

19: Linear algebra with polynomials 46:14

20: Bases of polynomial spaces 59:50

21: More bases of polynomial spaces 45:52

22: Polynomials and sequence spaces 1:00:49

23: Stirling numbers and Pascal triangles 58:45

24: Cubic splines (Bezier curves) using linear algebra 32:35

25: Cubic splines using calculus 41:42

26: Change of basis and Taylor coefficient vectors 50:31

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