I'm a bit confused about rotation and reflection matrices

In summary, the conversation discusses how to create a matrix for a rotation or reflection about a certain plane in R3. The process involves looking at the transition of e_1, e_2, and e_3 and plugging them into the columns of the matrix. This is how you can find the columns of the matrix representing any linear transformation.
  • #1
PirateFan308
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Homework Statement


I have a final coming up and I am a bit fuzzy on how to create a matrix that represents a rotation or reflection about a certain plane (in R3). Say we are given a rotation/reflection about either a plane or a line through two points T(v)=Av and we are told to find A. Do we simply have to look at [itex]e_1, e_2, e_3[/itex] and see what the transition would be for these vectors and plug the 'transitioned' [itex]e_1, e_2, e_3[/itex] into the columns of A, respectively? Or is there a lot more that I am missing? Thanks!
 
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  • #2
Yup, that's how you find the columns of the matrix representing any linear transformation.
 

Related to I'm a bit confused about rotation and reflection matrices

1. What is a rotation matrix?

A rotation matrix is a square matrix that represents a rotation transformation in a coordinate system. It is used to rotate points or objects in a 2D or 3D space around a fixed point called the origin.

2. How do rotation matrices work?

Rotation matrices use trigonometric functions to determine the new coordinates of a point after it has been rotated by a certain angle. The matrix is multiplied by the original coordinates to obtain the new rotated coordinates.

3. What is the difference between rotation and reflection matrices?

A rotation matrix is used to rotate points or objects in a coordinate system, while a reflection matrix is used to reflect points or objects across a line or plane. Both matrices are square matrices, but they have different values and operations.

4. How do you create a rotation matrix for a specific angle?

To create a rotation matrix, the angle of rotation must be known. The matrix elements can then be calculated using trigonometric functions such as sine and cosine. The resulting matrix will have a specific form depending on the dimensions of the coordinate system.

5. Can rotation matrices be used in 3D space?

Yes, rotation matrices can be used in 3D space. In 3D, rotation matrices are 3x3 matrices that can rotate points or objects around any axis in the coordinate system. The same principles of trigonometry apply, but the calculations are more complex due to the added dimension.

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