Applications of 3x3 Matrices - Wild Linear Algebra A

Applications of 3x3 Matrices - Wild Linear Algebra A

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pg 9: @ parallel projection of a vector u onto a plane at arbitrary projection direction l;

9 of 27

9 of 27

pg 9: @ parallel projection of a vector u onto a plane at arbitrary projection direction l;

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Applications of 3x3 Matrices - Wild Linear Algebra A

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  1. 1 CONTENT SUMMARY: pg 1: @ matrix/vector multiplication; Two interpretations: linear transformation/Change of coordinates; active vs passive approach;
  2. 2 pg 2: @ linear transformation approach; example; columns of transformation matrix are the 3 basis vectors transformed;
  3. 3 pg 3: @ Identity transformation; dilations scales the entire space; dilations are a closed system under composition and addition; remark on diagonal matrices and rational numbers;
  4. 4 pg 4: @ mixed dilations; Mixed dilations are also a closed system under composition and addition;
  5. 5 pg 5: @ examples; easy reflections; reflection in a plane; reflection in a line;
  6. 6 pg 6: @ examples: easy projections; projection to a plane; projection to a line;
  7. 7 pg 7: @ examples: easy rotations;
  8. 8 pg 8: @ Rational rotations; half-turn formulation;
  9. 9 pg 9: @ parallel projection of a vector u onto a plane at arbitrary projection direction l;
  10. 10 pg 10: @ The parallel projection matrix; projection properties;
  11. 11 pg 11: @ projection example continued; projecting u onto the line l; remark that the resulting matrix is rank 1;
  12. 12 pg 12: @ A general reflection in a plane;
  13. 13 pg 13: @ A general reflection in a line;
  14. 14 pg 14: @ response of the general formulas in the case of perpendicular projection and reflection; introducing the notion of perpendicularity; the normal vector to a plane is read off as the coefficie…
  15. 15 pg 15: @46:26 revisit of the general formulas; the quadrance of the vector mentioned @48:20 ; remark on the benefits of abstraction @ ;
  16. 16 pg 16 @ exercises 11.1:2 ; THANKS to EmptySpaceEnterprise
  17. 17 Introduction
  18. 18 Identity transformation, dilations
  19. 19 Mixed dilations
  20. 20 Easy reflections
  21. 21 Easy projections
  22. 22 Easy Rotations
  23. 23 Rational Rotations
  24. 24 Projection onto plane
  25. 25 Projection onto line
  26. 26 Reflection T across line l
  27. 27 Perpendicular projections and reflection

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