Linear Algebra Example Problems - Linear Transformations: Rotation and Reflection

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A linear transformation T: R2 to R2 is examined in this video. For this type of transformation, both the input vectors and output vectors are length 2 and can be easily plotted/visualized in a 2-D coordinate plane.

We find the matrix representation of a linear transformation that rotates points clockwise about the origin by pi/6 radians and then reflects the point through the line x1 = -x2. We also visualize the output of this transformation when the input is the vector x = [1; 0].

  1. Adam Panagos
  2. linear transformation reflection through a line
  3. linear transformation reflection
  4. linear transformation reflection across line
  5. linear transformation examples rotations in r2
  6. linear transformation reflection x-axis
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Комментарии
Автор

You should do counterclockwise instead of clockwise as your angle is positive

sumaia
Автор

could you explain a litttle more about the Aref, why is it 0, -1? When I put in (1, 0) e1 then I get 1, 0 and after i reflect it so it will be 0, 1

MySteamcracker
Автор

Thanks alot this was exactly what I was searching for :) Short and concise, but to the point and exceedingly well explained.
I have a question, your reflection matrix (Aref) has a negative determinant. Is this always the case with reflection matricies?
I think I have read that somewhere, that a negative determinant means just a reflection upon the plane (Since a negative area change makes no sense).

Thanks in advance and warm regards from Sweden.

taggebagge
Автор

And you said when it is clockwise, the negative sin should be in second row....but you are wrong.when it is counterclockwise then the negative sin should be in second row. Overall your method was right but you say things in a wrong way

sumaia