Applications of 3x3 Matrices - Wild Linear Algebra A

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