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CONTENT SUMMARY: pg 1: @ Linear algebra applied to polynomials; polynomials;
pg 2: @ a general polynomial; associated polynomial function; example;
pg 3: @ importance of polynomial functions;
pg 4: @ Interpolation;
pg 5: @12:23 finding a polynomial going through one point/two points; example; pg 6: @ example continued;
pg 7: @ example find the line through 2 points;
pg 8: @20:47 find the polynomial through 3 points; Vandermonde matrix @22:40 ; the pattern @;
pg 9: @ Regression statistics; looking for an approximate solution;
pg 10: @ Regression continued;
pg 11: @30:09 Linear regression; remark on the power of linear algebra @;
pg 12: @ Spaces; the connection between polynomials and linear algebra; operations; similarity of polynomials and vectors;
pg 13: @35:48 trying to say this object is like this object; mapping: start out with a polynomial and end up with a vector of coefficients @37:24 ; isomorphism; vector of coefficients; bijection @ ; surjective; injective;
pg 14: @ connection between functions and an abstract 3d vector space;
pg 15: @ Exercises19.1-3;
pg 16: @ Exercise 19.4; THANKS to EmptySpaceEnterprise
Introduction
A polynomial determines a polynomial function
Importance of polynomial functions
Interpolation
One point
Augmented matrix approach
Three points polynomial through
Regression
Linear regression
Polynomial spaces
Connection between functions and an abstract 3d vector space
Insights into Mathematics
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