Finding Projection Matrix in 3D Space
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How would I go about finding a projection matrix? As an example, how would I find the projection matrix $mathbf P$:
$mathbf{P} mathbf{v} = text{The projection of $mathbf{v}$ onto } begin{pmatrix} 0 \ 1 \ 0 end{pmatrix}$
I've no idea as to how to start.
Thanks for the help!
matrices projection-matrices
asked Nov 2 at 21:46
user588857
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up vote
-1
down vote
favorite
How would I go about finding a projection matrix? As an example, how would I find the projection matrix $mathbf P$:
$mathbf{P} mathbf{v} = text{The projection of $mathbf{v}$ onto } begin{pmatrix} 0 \ 1 \ 0 end{pmatrix}$
I've no idea as to how to start.
Thanks for the help!
matrices projection-matrices
asked Nov 2 at 21:46
user588857
285
1
Possible duplicate of Writing projection in terms of projection matrix
– gimusi
Nov 2 at 21:50
You can find many duplicates of that question also using Approach0
– gimusi
Nov 2 at 21:51
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
How would I go about finding a projection matrix? As an example, how would I find the projection matrix $mathbf P$:
$mathbf{P} mathbf{v} = text{The projection of $mathbf{v}$ onto } begin{pmatrix} 0 \ 1 \ 0 end{pmatrix}$
I've no idea as to how to start.
Thanks for the help!
matrices projection-matrices
asked Nov 2 at 21:46
user588857
285
How would I go about finding a projection matrix? As an example, how would I find the projection matrix $mathbf P$:
$mathbf{P} mathbf{v} = text{The projection of $mathbf{v}$ onto } begin{pmatrix} 0 \ 1 \ 0 end{pmatrix}$
I've no idea as to how to start.
Thanks for the help!
matrices projection-matrices
matrices projection-matrices
asked Nov 2 at 21:46
user588857
285
asked Nov 2 at 21:46
user588857
285
asked Nov 2 at 21:46
user588857
285
asked Nov 2 at 21:46
user588857
285
asked Nov 2 at 21:46
user588857
285
285
1
Possible duplicate of Writing projection in terms of projection matrix
– gimusi
Nov 2 at 21:50
You can find many duplicates of that question also using Approach0
– gimusi
Nov 2 at 21:51
add a comment |
1
Possible duplicate of Writing projection in terms of projection matrix
– gimusi
Nov 2 at 21:50
You can find many duplicates of that question also using Approach0
– gimusi
Nov 2 at 21:51
1
1
Possible duplicate of Writing projection in terms of projection matrix
– gimusi
Nov 2 at 21:50
Possible duplicate of Writing projection in terms of projection matrix
– gimusi
Nov 2 at 21:50
You can find many duplicates of that question also using Approach0
– gimusi
Nov 2 at 21:51
You can find many duplicates of that question also using Approach0
– gimusi
Nov 2 at 21:51
add a comment |
1 Answer
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Any $3times 1$ vector can be expressed as the linear combination of the basis as following $$v=(v_1,v_2,v_3)=v_1(1,0,0)+v_2(0,1,0)+v_3(0,0,1)$$by projection on a fixed vector, we always mean that we preserve the component of any vector to be projected along the given fixed vector i.e. $$Pv=text{the component of }vtext{ along the vector }(0,1,0)=v_2(0,1,0)$$Here is the desired projection matrix $P$ $$P=begin{bmatrix}0&0&0\0&1&0\0&0&0end{bmatrix}$$
answered Nov 24 at 17:20
Mostafa Ayaz
13.4k3836
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Any $3times 1$ vector can be expressed as the linear combination of the basis as following $$v=(v_1,v_2,v_3)=v_1(1,0,0)+v_2(0,1,0)+v_3(0,0,1)$$by projection on a fixed vector, we always mean that we preserve the component of any vector to be projected along the given fixed vector i.e. $$Pv=text{the component of }vtext{ along the vector }(0,1,0)=v_2(0,1,0)$$Here is the desired projection matrix $P$ $$P=begin{bmatrix}0&0&0\0&1&0\0&0&0end{bmatrix}$$
answered Nov 24 at 17:20
Mostafa Ayaz
13.4k3836
add a comment |
up vote
0
down vote
Any $3times 1$ vector can be expressed as the linear combination of the basis as following $$v=(v_1,v_2,v_3)=v_1(1,0,0)+v_2(0,1,0)+v_3(0,0,1)$$by projection on a fixed vector, we always mean that we preserve the component of any vector to be projected along the given fixed vector i.e. $$Pv=text{the component of }vtext{ along the vector }(0,1,0)=v_2(0,1,0)$$Here is the desired projection matrix $P$ $$P=begin{bmatrix}0&0&0\0&1&0\0&0&0end{bmatrix}$$
answered Nov 24 at 17:20
Mostafa Ayaz
13.4k3836
add a comment |
up vote
0
down vote
up vote
0
down vote
Any $3times 1$ vector can be expressed as the linear combination of the basis as following $$v=(v_1,v_2,v_3)=v_1(1,0,0)+v_2(0,1,0)+v_3(0,0,1)$$by projection on a fixed vector, we always mean that we preserve the component of any vector to be projected along the given fixed vector i.e. $$Pv=text{the component of }vtext{ along the vector }(0,1,0)=v_2(0,1,0)$$Here is the desired projection matrix $P$ $$P=begin{bmatrix}0&0&0\0&1&0\0&0&0end{bmatrix}$$
answered Nov 24 at 17:20
Mostafa Ayaz
13.4k3836
Any $3times 1$ vector can be expressed as the linear combination of the basis as following $$v=(v_1,v_2,v_3)=v_1(1,0,0)+v_2(0,1,0)+v_3(0,0,1)$$by projection on a fixed vector, we always mean that we preserve the component of any vector to be projected along the given fixed vector i.e. $$Pv=text{the component of }vtext{ along the vector }(0,1,0)=v_2(0,1,0)$$Here is the desired projection matrix $P$ $$P=begin{bmatrix}0&0&0\0&1&0\0&0&0end{bmatrix}$$
answered Nov 24 at 17:20
Mostafa Ayaz
13.4k3836
answered Nov 24 at 17:20
Mostafa Ayaz
13.4k3836
answered Nov 24 at 17:20
Mostafa Ayaz
13.4k3836
answered Nov 24 at 17:20
Mostafa Ayaz
13.4k3836
13.4k3836
add a comment |
add a comment |
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Possible duplicate of Writing projection in terms of projection matrix
– gimusi
Nov 2 at 21:50
You can find many duplicates of that question also using Approach0
– gimusi
Nov 2 at 21:51