- #1
Matrix geometric representation
- Thread starter SunGod87
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Homework Help Overview
The discussion revolves around the transformation of coordinates using matrices, specifically how a given matrix can be used to transform a set of coordinates (x_1, y_1, z_1) into another set (x_2, y_2, z_2). The original poster expresses uncertainty about the complexity of the resulting matrix in relation to their coursework.
Discussion Character
- Exploratory, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- Participants discuss the process of multiplying matrices to achieve the desired coordinate transformation. There are questions about the clarity of the original poster's intentions and the correctness of their matrix operations. Some participants suggest verifying the multiplication of matrices and the resulting transformations.
Discussion Status
The discussion has evolved with the original poster clarifying their approach and expressing some confusion regarding the complexity of the matrix they derived. They have also indicated a resolution to their initial query, although the correctness of their notation and interpretation remains open for further discussion.
Contextual Notes
There is mention of the coursework level, suggesting that the complexity of the matrix may not align with what has been covered in class. The original poster's notation is also noted as potentially needing clarification.
- #2
HallsofIvy
Science Advisor
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Do you mean that you want to show that this matrix will transform a given set of co-ordinates (x_1, y_1, z_1) to a given set of coordinates (x_2, y_2, z_2)?
If so, then the obvious: multiply the given matrix by the given (x_1, y_1, z_1) and see that they give (x_2, y_2, z_2). If either set of coordinates is not given then I don't understand what you want to do. Obviously multiplying a matrix by a point (represented as a column matrix) will give another point.
If so, then the obvious: multiply the given matrix by the given (x_1, y_1, z_1) and see that they give (x_2, y_2, z_2). If either set of coordinates is not given then I don't understand what you want to do. Obviously multiplying a matrix by a point (represented as a column matrix) will give another point.
- #3
SunGod87
- 30
- 0
Sorry, it will be easier if I just post the question.
What I've done is written two equations
r2 = r1.A
r3 = r2.B
Where A and B are the matrices representing the two transformations.
Then I have written r3 = r1.A.B
which expresses the components of r3 in terms of r1.
After multiplying the two matrices I got the matrix I attached to my first post. However this new matrix looks a little too advanced for what we've been doing in the course. So maybe I've made a mistake?
What I've done is written two equations
r2 = r1.A
r3 = r2.B
Where A and B are the matrices representing the two transformations.
Then I have written r3 = r1.A.B
which expresses the components of r3 in terms of r1.
After multiplying the two matrices I got the matrix I attached to my first post. However this new matrix looks a little too advanced for what we've been doing in the course. So maybe I've made a mistake?
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- #4
SunGod87
- 30
- 0
Nevermind now I have managed to do it.
r2 = A.r1
r3 = B.r2
r3 = B.A.r1
And I get B.A = (0,1,0), (-1,0,0), (0,0,1)
Hopefully my notation is okay here, it's meant to read like: (a_11, a_12, a_13), (a_21, a_22, a_23), (a_31, a_32, a_33)
Which indicates a rotation of 90 degrees clockwise about the z-axis (going from r1 to r3), right?
r2 = A.r1
r3 = B.r2
r3 = B.A.r1
And I get B.A = (0,1,0), (-1,0,0), (0,0,1)
Hopefully my notation is okay here, it's meant to read like: (a_11, a_12, a_13), (a_21, a_22, a_23), (a_31, a_32, a_33)
Which indicates a rotation of 90 degrees clockwise about the z-axis (going from r1 to r3), right?
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