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The kernel property
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The Geometry of a System of Linear Equations - Wild Linear Algebra A
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- 1 CONTENT SUMMARY: pg 1: @ The geometry of a system of linear equations; m linear equations in n variables;
- 2 pg 2: @ The picture to keep in mind; The big picture;
- 3 pg 3: @05:00 The kernel property; property versus set; remark on fundamental issue @ see "math foundations" series;
- 4 pg 4: @ examples; what is a line?; what is a circle; properties instead of infinite sets;
- 5 pg 5: @ managing properties; statement of Properties moral;
- 6 pg 6: @ examples; properties of a 3-d vector;
- 7 pg 7: @ Subspace properties; Definition and examples;
- 8 pg 8: @ subspace properties of 2-d vectors;
- 9 pg 9: @ subspace properties of 3-d vectors;
- 10 pg 10: @ Definition of kernel property; definition of image property; Theorem 1; Theorem 2;
- 11 pg 11: @ Theorem proofs;
- 12 pg 12: @32:05 subspaces in higher dimensional spaces; spanning set; equation set; hyperplane @ ;
- 13 pg 13: @ Linear transformation n-dim to m-dim; pg13_Theorem ;
- 14 pg 14: @ proof of pg13_Theorem;
- 15 pg 15: @ example 2d to 2d;
- 16 pg 16: @ example 3d to 2d;
- 17 pg 17: @ example 3d to 3d;
- 18 pg 18: @1:03:13 example continued; remark: typifies a linear transformation @;
- 19 pg 19: @ exercise 18.1;
- 20 pg 20: @ exercise 18.2; THANKS to EmptySpaceEnterprise
- 21 Introduction
- 22 The kernel property
- 23 What is a line? What is a circle;
- 24 Managing properties
- 25 Properties of vectors
- 26 Subspace properties
- 27 Subspaces of V²
- 28 Subspaces of V³
- 29 Definition of kernel property
- 30 subspaces in higher dimensional spaces
- 31 Linear transformation n-dim to m-dim
