3-D Rotation Matrix [on hold]
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Question says what constraints must the elements (R ij) of three dimensional rotation matrix satisfy in order to preserve the length of a vector A(for all vectors A).
I don't get why, at all would axes transformations change the magnitude of a vector?
vectors matrix-calculus geometric-transformation matrix-analysis
asked yesterday
Onkar Singh
41
put on hold as off-topic by Saad, Leucippus, user91500, Paul Frost, José Carlos Santos 19 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Leucippus, user91500, Paul Frost, José Carlos Santos
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Question says what constraints must the elements (R ij) of three dimensional rotation matrix satisfy in order to preserve the length of a vector A(for all vectors A).
I don't get why, at all would axes transformations change the magnitude of a vector?
vectors matrix-calculus geometric-transformation matrix-analysis
asked yesterday
Onkar Singh
41
put on hold as off-topic by Saad, Leucippus, user91500, Paul Frost, José Carlos Santos 19 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Leucippus, user91500, Paul Frost, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
Well, consider 3D transformation matrix $$mathbf{M} = left [ begin{matrix} 2 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 2 end{matrix} right ]$$It is a transformation: it doubles the length of all nonzero vectors.
– Nominal Animal
yesterday
I was looking for proper sources, but couldn't find any, so instead of providing an answer, I'll just comment that pure rotation matrices are orthonormal: all row vectors form an orthonormal basis set, and all column vectors form an orthonormal basis set. The result of those requirements is that such matrices have determinant +1, and the inverse of such matrices is equal to their transpose.
– Nominal Animal
yesterday
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Question says what constraints must the elements (R ij) of three dimensional rotation matrix satisfy in order to preserve the length of a vector A(for all vectors A).
I don't get why, at all would axes transformations change the magnitude of a vector?
vectors matrix-calculus geometric-transformation matrix-analysis
asked yesterday
Onkar Singh
41
Question says what constraints must the elements (R ij) of three dimensional rotation matrix satisfy in order to preserve the length of a vector A(for all vectors A).
I don't get why, at all would axes transformations change the magnitude of a vector?
vectors matrix-calculus geometric-transformation matrix-analysis
vectors matrix-calculus geometric-transformation matrix-analysis
asked yesterday
Onkar Singh
41
asked yesterday
Onkar Singh
41
asked yesterday
Onkar Singh
41
asked yesterday
Onkar Singh
41
asked yesterday
Onkar Singh
41
41
put on hold as off-topic by Saad, Leucippus, user91500, Paul Frost, José Carlos Santos 19 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Leucippus, user91500, Paul Frost, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Saad, Leucippus, user91500, Paul Frost, José Carlos Santos 19 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Leucippus, user91500, Paul Frost, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
Well, consider 3D transformation matrix $$mathbf{M} = left [ begin{matrix} 2 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 2 end{matrix} right ]$$It is a transformation: it doubles the length of all nonzero vectors.
– Nominal Animal
yesterday
I was looking for proper sources, but couldn't find any, so instead of providing an answer, I'll just comment that pure rotation matrices are orthonormal: all row vectors form an orthonormal basis set, and all column vectors form an orthonormal basis set. The result of those requirements is that such matrices have determinant +1, and the inverse of such matrices is equal to their transpose.
– Nominal Animal
yesterday
add a comment |
Well, consider 3D transformation matrix $$mathbf{M} = left [ begin{matrix} 2 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 2 end{matrix} right ]$$It is a transformation: it doubles the length of all nonzero vectors.
– Nominal Animal
yesterday
I was looking for proper sources, but couldn't find any, so instead of providing an answer, I'll just comment that pure rotation matrices are orthonormal: all row vectors form an orthonormal basis set, and all column vectors form an orthonormal basis set. The result of those requirements is that such matrices have determinant +1, and the inverse of such matrices is equal to their transpose.
– Nominal Animal
yesterday
Well, consider 3D transformation matrix $$mathbf{M} = left [ begin{matrix} 2 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 2 end{matrix} right ]$$It is a transformation: it doubles the length of all nonzero vectors.
– Nominal Animal
yesterday
Well, consider 3D transformation matrix $$mathbf{M} = left [ begin{matrix} 2 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 2 end{matrix} right ]$$It is a transformation: it doubles the length of all nonzero vectors.
– Nominal Animal
yesterday
I was looking for proper sources, but couldn't find any, so instead of providing an answer, I'll just comment that pure rotation matrices are orthonormal: all row vectors form an orthonormal basis set, and all column vectors form an orthonormal basis set. The result of those requirements is that such matrices have determinant +1, and the inverse of such matrices is equal to their transpose.
– Nominal Animal
yesterday
I was looking for proper sources, but couldn't find any, so instead of providing an answer, I'll just comment that pure rotation matrices are orthonormal: all row vectors form an orthonormal basis set, and all column vectors form an orthonormal basis set. The result of those requirements is that such matrices have determinant +1, and the inverse of such matrices is equal to their transpose.
– Nominal Animal
yesterday
add a comment |
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Well, consider 3D transformation matrix $$mathbf{M} = left [ begin{matrix} 2 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 2 end{matrix} right ]$$It is a transformation: it doubles the length of all nonzero vectors.
– Nominal Animal
yesterday
I was looking for proper sources, but couldn't find any, so instead of providing an answer, I'll just comment that pure rotation matrices are orthonormal: all row vectors form an orthonormal basis set, and all column vectors form an orthonormal basis set. The result of those requirements is that such matrices have determinant +1, and the inverse of such matrices is equal to their transpose.
– Nominal Animal
yesterday