# Linear Algebra

The University of New South Wales,

Updated On 02 Feb, 19

The University of New South Wales,

Updated On 02 Feb, 19

This course on Linear Algebra is meant for first year undergraduates or college students. It presents the subject in a visual geometric way, with special orientation to applications and understanding of key concepts. The subject naturally sits inside affine algebraic geometry. Flexibility in choosing coordinate frameworks is essential for understanding the subject. Determinants also play an important role, and these are introduced in the context of multi-vectors in the sense of Grassmann. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.

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4.1 ( 11 )

Spaces of polynomials provide important applications of linear algebra. Here we introduce polynomials and the associated polynomial functions (we prefer to keep these separate in our minds).

Polynomials are vital in interpolation, and we show how this works. Then we explain how regression in statistics (both linear and non-linear) can be viewed using our geometric approach to a linear transformation.

Finally we discuss the use of `isomorphism to relate the space of polynomials up to a certain fixed degree to our more familiar space of column vectors of a certain size.

CONTENT SUMMARY pg 1 @0008 Linear algebra applied to polynomials; polynomials;

pg 2 @0333 a general polynomial; associated polynomial function; example;

pg 3 @0735 importance of polynomial functions;

pg 4 @1037 Interpolation;

pg 5 @1223 finding a polynomial going through one pointtwo points; example; pg 6 @1444 example continued;

pg 7 @1811 example (find the line through 2 points);

pg 8 @2047 (find the polynomial through 3 points); Vandermonde matrix @2240 ; the pattern @2411;

pg 9 @2502 Regression (statistics); looking for an approximate solution;

pg 10 @2659 Regression continued;

pg 11 @3009 Linear regression; remark on the power of linear algebra @3239;

pg 12 @3304 Spaces; the connection between polynomials and linear algebra; operations; similarity of polynomials and vectors;

pg 13 @3548 trying to say this object is like this object; mapping start out with a polynomial and end up with a vector of coefficients @3724 ; isomorphism; vector of coefficients; bijection @3807 ; surjective; injective;

pg 14 @4046 connection between functions and an abstract 3d vector space;

pg 15 @4336 Exercises19.1-3;

pg 16 @4451 Exercise 19.4; (THANKS to EmptySpaceEnterprise)

Sam

Sep 12, 2018

Excellent course helped me understand topic that i couldn't while attendinfg my college.

Dembe

March 29, 2019

Great course. Thank you very much.