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Homework Statement
Which matrix represents a rotation?
Homework Equations
The Attempt at a Solution
It seems odd that this matrix has somewhat the form for rotation about z-axis, just that you need to swap the cos θ for the sin θ.
You didn't show very much work.It seems odd that this matrix has somewhat the form for rotation about z-axis, just that you need to swap the cos θ for the sin θ.
The first matrix is the rotation matrix. It is a rotation matrix about z-axis.You didn't show very much work.
Before I help you further, did you solve the first two parts of the problem?
- Identifying which one of those two matrices represents a rotation, and
- For that matrix, finding the angle and axis of revolution.
If you didn't, do you know how to identify whether a matrix represents a rotation? Do you know how to find the eigenrotation (angle and axis of revolution) for a rotation matrix?
Through what angle? And what is your reasoning?The first matrix is the rotation matrix. It is a rotation matrix about z-axis.
I have no idea what you mean by this. What do you mean by [1, 1] and in what sense is it equal to the number -1/2? Did you look at what the vectors (1, 0, 0) and (0, 1, 0) are mapped to?My problem here is that the diagonals of a rotation matrix should be equal! But here clearly it's not as [1,1] = -1/2 while [2,2] = 1/2
I think that what he means is that each of the three primitive rotations in 3 dimensional space (rotations about the x, y, and z axes) have a matrix in which one of the diagonal elements is 1 and the other two are equal to one another.I have no idea what you mean by this. What do you mean by [1, 1] and in what sense is it equal to the number -1/2?My problem here is that the diagonals of a rotation matrix should be equal! But here clearly it's not as [1,1] = -1/2 while [2,2] = 1/2
Sorry, by [1,1] i meant the 1st row, 1st column number.Through what angle? And what is your reasoning?
I have no idea what you mean by this. What do you mean by [1, 1] and in what sense is it equal to the number -1/2? Did you look at what the vectors (1, 0, 0) and (0, 1, 0) are mapped to?
A^{T} = I.I think that what he means is that each of the three primitive rotations in 3 dimensional space (rotations about the x, y, and z axes) have a matrix in which one of the diagonal elements is 1 and the other two are equal to one another.
That clearly isn't the case here.
So maybe this isn't a rotation matrix. Perhaps it's that ugly beast to the right that is the rotation matrix.
A rotation about what? Notice that the 3,3 element is 1. There's no reflection in the x-y plane here.Hence it is a rotation, followed by a reflection in the x-y plane.