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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 @ ; …

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

Description:

Explore the application of linear algebra to polynomials in this 46-minute lecture. Delve into the world of polynomials and their associated functions, understanding their vital role in interpolation. Learn how to find polynomials passing through specific points and discover the power of the Vandermonde matrix. Examine regression in statistics from a geometric perspective, focusing on both linear and non-linear approaches. Investigate the concept of isomorphism, connecting polynomial spaces to familiar column vector spaces. Gain insights into the relationship between functions and abstract vector spaces. Practice with provided exercises to reinforce your understanding of these fundamental concepts in linear algebra and polynomial theory.

Linear Algebra With Polynomials - Wild Linear Algebra A

Insights into Mathematics

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#Mathematics #Algebra #Linear Algebra #Polynomials #Statistics & Probability #Statistical Modeling #Regression Analysis #Interpolation #Vector Spaces #Linear Transformations #Polynomial Functions #Group Theory #Isomorphisms

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