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CONTENT SUMMARY: pg 1: @ matrix/vector multiplication; Two interpretations: linear transformation/Change of coordinates; active vs passive approach;
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Applications of 3x3 Matrices - Wild Linear Algebra A
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- 1 CONTENT SUMMARY: pg 1: @ matrix/vector multiplication; Two interpretations: linear transformation/Change of coordinates; active vs passive approach;
- 2 pg 2: @ linear transformation approach; example; columns of transformation matrix are the 3 basis vectors transformed;
- 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 pg 4: @ mixed dilations; Mixed dilations are also a closed system under composition and addition;
- 5 pg 5: @ examples; easy reflections; reflection in a plane; reflection in a line;
- 6 pg 6: @ examples: easy projections; projection to a plane; projection to a line;
- 7 pg 7: @ examples: easy rotations;
- 8 pg 8: @ Rational rotations; half-turn formulation;
- 9 pg 9: @ parallel projection of a vector u onto a plane at arbitrary projection direction l;
- 10 pg 10: @ The parallel projection matrix; projection properties;
- 11 pg 11: @ projection example continued; projecting u onto the line l; remark that the resulting matrix is rank 1;
- 12 pg 12: @ A general reflection in a plane;
- 13 pg 13: @ A general reflection in a line;
- 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 pg 15: @46:26 revisit of the general formulas; the quadrance of the vector mentioned @48:20 ; remark on the benefits of abstraction @ ;
- 16 pg 16 @ exercises 11.1:2 ; THANKS to EmptySpaceEnterprise
- 17 Introduction
- 18 Identity transformation, dilations
- 19 Mixed dilations
- 20 Easy reflections
- 21 Easy projections
- 22 Easy Rotations
- 23 Rational Rotations
- 24 Projection onto plane
- 25 Projection onto line
- 26 Reflection T across line l
- 27 Perpendicular projections and reflection
