Mixing
New coordinates after rotation of axis around origin.
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
I have a point $(-24.75665066,0.61535793,34.60714434)inmathbbR^3$
I would like to find the new coordinate after a $3times3$ rotation matrix is applied to the axis, around the origin. Matrix example below:
$$
beginbmatrix
-0.4197673 & 0.5603373 & 0.7140151\
-0.8973154 & -0.1379305 & -0.4192854\
-0.1364568 & -0.8166990 & 0.5606980
endbmatrix
$$
This type of maths is way above my head, however trying to solve this problem is really encouraging me to go and study further mathematics. I was able to find some similar questions, but none I was able to use. Any insight would be much appreciated.
coordinate-systems polar-coordinates rotations
edited Jul 27 at 2:28
高田航
1,116318
asked Jul 27 at 2:11
Josh
11
add a comment |Â
up vote
0
down vote
favorite
I have a point $(-24.75665066,0.61535793,34.60714434)inmathbbR^3$
I would like to find the new coordinate after a $3times3$ rotation matrix is applied to the axis, around the origin. Matrix example below:
$$
beginbmatrix
-0.4197673 & 0.5603373 & 0.7140151\
-0.8973154 & -0.1379305 & -0.4192854\
-0.1364568 & -0.8166990 & 0.5606980
endbmatrix
$$
This type of maths is way above my head, however trying to solve this problem is really encouraging me to go and study further mathematics. I was able to find some similar questions, but none I was able to use. Any insight would be much appreciated.
coordinate-systems polar-coordinates rotations
edited Jul 27 at 2:28
高田航
1,116318
asked Jul 27 at 2:11
Josh
11
2
If $A$ is your matrix, and $x$ your vector, you do matrix multiplication to get the new coordinates: $x'=Ax.$
– Adrian Keister
Jul 27 at 2:12
As Adrian said, and to calculate $Ax$ you treat $x$ like a $3times 1$ matrix.
– M. Nestor
Jul 27 at 2:32
appreciate the responses, much simpler than I had imagined! Thank you
– Josh
Jul 27 at 2:40
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have a point $(-24.75665066,0.61535793,34.60714434)inmathbbR^3$
I would like to find the new coordinate after a $3times3$ rotation matrix is applied to the axis, around the origin. Matrix example below:
$$
beginbmatrix
-0.4197673 & 0.5603373 & 0.7140151\
-0.8973154 & -0.1379305 & -0.4192854\
-0.1364568 & -0.8166990 & 0.5606980
endbmatrix
$$
This type of maths is way above my head, however trying to solve this problem is really encouraging me to go and study further mathematics. I was able to find some similar questions, but none I was able to use. Any insight would be much appreciated.
coordinate-systems polar-coordinates rotations
edited Jul 27 at 2:28
高田航
1,116318
asked Jul 27 at 2:11
Josh
11
I have a point $(-24.75665066,0.61535793,34.60714434)inmathbbR^3$
I would like to find the new coordinate after a $3times3$ rotation matrix is applied to the axis, around the origin. Matrix example below:
$$
beginbmatrix
-0.4197673 & 0.5603373 & 0.7140151\
-0.8973154 & -0.1379305 & -0.4192854\
-0.1364568 & -0.8166990 & 0.5606980
endbmatrix
$$
This type of maths is way above my head, however trying to solve this problem is really encouraging me to go and study further mathematics. I was able to find some similar questions, but none I was able to use. Any insight would be much appreciated.
coordinate-systems polar-coordinates rotations
edited Jul 27 at 2:28
高田航
1,116318
asked Jul 27 at 2:11
Josh
11
edited Jul 27 at 2:28
高田航
1,116318
edited Jul 27 at 2:28
高田航
1,116318
edited Jul 27 at 2:28
高田航
1,116318
1,116318
asked Jul 27 at 2:11
Josh
11
asked Jul 27 at 2:11
Josh
11
asked Jul 27 at 2:11
Josh
11
11
2
If $A$ is your matrix, and $x$ your vector, you do matrix multiplication to get the new coordinates: $x'=Ax.$
– Adrian Keister
Jul 27 at 2:12
As Adrian said, and to calculate $Ax$ you treat $x$ like a $3times 1$ matrix.
– M. Nestor
Jul 27 at 2:32
appreciate the responses, much simpler than I had imagined! Thank you
– Josh
Jul 27 at 2:40
add a comment |Â
2
If $A$ is your matrix, and $x$ your vector, you do matrix multiplication to get the new coordinates: $x'=Ax.$
– Adrian Keister
Jul 27 at 2:12
As Adrian said, and to calculate $Ax$ you treat $x$ like a $3times 1$ matrix.
– M. Nestor
Jul 27 at 2:32
appreciate the responses, much simpler than I had imagined! Thank you
– Josh
Jul 27 at 2:40
2
2
If $A$ is your matrix, and $x$ your vector, you do matrix multiplication to get the new coordinates: $x'=Ax.$
– Adrian Keister
Jul 27 at 2:12
If $A$ is your matrix, and $x$ your vector, you do matrix multiplication to get the new coordinates: $x'=Ax.$
– Adrian Keister
Jul 27 at 2:12
As Adrian said, and to calculate $Ax$ you treat $x$ like a $3times 1$ matrix.
– M. Nestor
Jul 27 at 2:32
As Adrian said, and to calculate $Ax$ you treat $x$ like a $3times 1$ matrix.
– M. Nestor
Jul 27 at 2:32
appreciate the responses, much simpler than I had imagined! Thank you
– Josh
Jul 27 at 2:40
appreciate the responses, much simpler than I had imagined! Thank you
– Josh
Jul 27 at 2:40
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
If $A$ is an $mtimes n$ matrix, then $f(x)=Avecx$ where $vecxinmathbbR^n$ describes a linear map $mathbbR^nrightarrowmathbbR^m$.
From your description, it seems that you are working with a $3times 3$ rotation matrix, which sends vectors (or your "coordinate") in $mathbbR^3rightarrowmathbbR^3$.
Therefore, to apply the transformation to your point, simply express the point as a $3times 1$ vector, and right-multiply it to the rotation matrix:
$$
beginbmatrix
-0.4197673 & 0.5603373 & 0.7140151\
-0.8973154 & -0.1379305 & -0.4192854\
-0.1364568 & -0.8166990 & 0.5606980
endbmatrix times
beginbmatrix
-24.75665066 \
0.61535793\
34.60714434\
endbmatrix
$$
to obtain the new vector
$$
beginbmatrix
35.446864032260734\
7.619376905219662\
22.279807738857738
endbmatrix
$$
answered Jul 27 at 2:37
高田航
1,116318
1
thank you so much!
– Josh
Jul 27 at 2:39
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
If $A$ is an $mtimes n$ matrix, then $f(x)=Avecx$ where $vecxinmathbbR^n$ describes a linear map $mathbbR^nrightarrowmathbbR^m$.
From your description, it seems that you are working with a $3times 3$ rotation matrix, which sends vectors (or your "coordinate") in $mathbbR^3rightarrowmathbbR^3$.
Therefore, to apply the transformation to your point, simply express the point as a $3times 1$ vector, and right-multiply it to the rotation matrix:
$$
beginbmatrix
-0.4197673 & 0.5603373 & 0.7140151\
-0.8973154 & -0.1379305 & -0.4192854\
-0.1364568 & -0.8166990 & 0.5606980
endbmatrix times
beginbmatrix
-24.75665066 \
0.61535793\
34.60714434\
endbmatrix
$$
to obtain the new vector
$$
beginbmatrix
35.446864032260734\
7.619376905219662\
22.279807738857738
endbmatrix
$$
answered Jul 27 at 2:37
高田航
1,116318
1
thank you so much!
– Josh
Jul 27 at 2:39
add a comment |Â
up vote
1
down vote
If $A$ is an $mtimes n$ matrix, then $f(x)=Avecx$ where $vecxinmathbbR^n$ describes a linear map $mathbbR^nrightarrowmathbbR^m$.
From your description, it seems that you are working with a $3times 3$ rotation matrix, which sends vectors (or your "coordinate") in $mathbbR^3rightarrowmathbbR^3$.
Therefore, to apply the transformation to your point, simply express the point as a $3times 1$ vector, and right-multiply it to the rotation matrix:
$$
beginbmatrix
-0.4197673 & 0.5603373 & 0.7140151\
-0.8973154 & -0.1379305 & -0.4192854\
-0.1364568 & -0.8166990 & 0.5606980
endbmatrix times
beginbmatrix
-24.75665066 \
0.61535793\
34.60714434\
endbmatrix
$$
to obtain the new vector
$$
beginbmatrix
35.446864032260734\
7.619376905219662\
22.279807738857738
endbmatrix
$$
answered Jul 27 at 2:37
高田航
1,116318
1
thank you so much!
– Josh
Jul 27 at 2:39
add a comment |Â
up vote
1
down vote
up vote
1
down vote
If $A$ is an $mtimes n$ matrix, then $f(x)=Avecx$ where $vecxinmathbbR^n$ describes a linear map $mathbbR^nrightarrowmathbbR^m$.
From your description, it seems that you are working with a $3times 3$ rotation matrix, which sends vectors (or your "coordinate") in $mathbbR^3rightarrowmathbbR^3$.
Therefore, to apply the transformation to your point, simply express the point as a $3times 1$ vector, and right-multiply it to the rotation matrix:
$$
beginbmatrix
-0.4197673 & 0.5603373 & 0.7140151\
-0.8973154 & -0.1379305 & -0.4192854\
-0.1364568 & -0.8166990 & 0.5606980
endbmatrix times
beginbmatrix
-24.75665066 \
0.61535793\
34.60714434\
endbmatrix
$$
to obtain the new vector
$$
beginbmatrix
35.446864032260734\
7.619376905219662\
22.279807738857738
endbmatrix
$$
answered Jul 27 at 2:37
高田航
1,116318
If $A$ is an $mtimes n$ matrix, then $f(x)=Avecx$ where $vecxinmathbbR^n$ describes a linear map $mathbbR^nrightarrowmathbbR^m$.
From your description, it seems that you are working with a $3times 3$ rotation matrix, which sends vectors (or your "coordinate") in $mathbbR^3rightarrowmathbbR^3$.
Therefore, to apply the transformation to your point, simply express the point as a $3times 1$ vector, and right-multiply it to the rotation matrix:
$$
beginbmatrix
-0.4197673 & 0.5603373 & 0.7140151\
-0.8973154 & -0.1379305 & -0.4192854\
-0.1364568 & -0.8166990 & 0.5606980
endbmatrix times
beginbmatrix
-24.75665066 \
0.61535793\
34.60714434\
endbmatrix
$$
to obtain the new vector
$$
beginbmatrix
35.446864032260734\
7.619376905219662\
22.279807738857738
endbmatrix
$$
answered Jul 27 at 2:37
高田航
1,116318
answered Jul 27 at 2:37
高田航
1,116318
answered Jul 27 at 2:37
高田航
1,116318
answered Jul 27 at 2:37
高田航
1,116318
1,116318
1
thank you so much!
– Josh
Jul 27 at 2:39
add a comment |Â
1
thank you so much!
– Josh
Jul 27 at 2:39
1
1
thank you so much!
– Josh
Jul 27 at 2:39
thank you so much!
– Josh
Jul 27 at 2:39
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2863984%2fnew-coordinates-after-rotation-of-axis-around-origin%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
2
If $A$ is your matrix, and $x$ your vector, you do matrix multiplication to get the new coordinates: $x'=Ax.$
– Adrian Keister
Jul 27 at 2:12
As Adrian said, and to calculate $Ax$ you treat $x$ like a $3times 1$ matrix.
– M. Nestor
Jul 27 at 2:32
appreciate the responses, much simpler than I had imagined! Thank you
– Josh
Jul 27 at 2:40