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CONTENT SUMMARY: pg 1: @00:08 Map of a space of polynomials to a space of vectors; Definition: linear/vector space; course distinction @ ;
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Bases of Polynomial Spaces - Wild Linear Algebra - NJ Wildberger
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- 1 CONTENT SUMMARY: pg 1: @00:08 Map of a space of polynomials to a space of vectors; Definition: linear/vector space; course distinction @ ;
- 2 pg 2: @ Definition: An ordered basis of a linear space; Example1 ;
- 3 pg 3: @ Example2 basis of a vector space; Example3 basis of a polynomial space; Definition: Dimension of a linear/vector space; examples;
- 4 pg 4: @09:25 The space of polynomials is richer than the isomorphic space of vectors; translating polynomials @ ; degree of the polynomial is preserved in translation;
- 5 pg 5: @13:20 Study01 of translation by 3 see previous page; A linear transformation @ ;
- 6 pg 6: @16:48 study01 continued; image and kernel of polynomial of degree 3 @;
- 7 pg 7: @ the derivative of a function appears in translation;
- 8 pg 8: @22:49 Definition: The derivative of a polynomial; calculus via linear algebra @;
- 9 pg 9: @ Calculus as algebra; pg9_Theorem product rule; proof Leibniz mentioned;
- 10 pg 10: @ Translating a polynomial and obtaining the derivatives; Taylor series mentioned;
- 11 pg 11: @ Importance of various bases; standard basis; factorial basis; Example ; coefficient vectors of a polynomial with respect to a basis;
- 12 pg 12: @42:10 Theorem Basis isomorphism correspondence; The standard vector space of column vectors @ ;
- 13 pg 13: @46:22 The derivative as a linear transformation; remark about formulas in calculus and combinatorics @ ;
- 14 pg 14: @ Another basis; the standard basis moved over by 3; example;
- 15 pg 15: @54:32 Change of basis matrix; How to get this matrix! @ ;
- 16 pg 16: @57:16 Exercises 20.1-3; closing remarks @; THANKS to EmptySpaceEnterprise
- 17 Introduction
- 18 Ordered basis of a linear space
- 19 Translation as a linear transformations
- 20 Derivative of a polynomial
- 21 Some bases of P³
- 22 Theorem Basis isomorphism correspondence
- 23 The derivative D as a linear transformation
- 24 Another basis
- 25 Change of basis matrix
