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In three dimensional euclidean space, can we take projection of a plane onto a plane

0

$begingroup$

I was reading about projection mapping in linear algebra between finite dimensional vector spaces. There were given a condition that my space should be written as direct sum of two of its subspaces V and W to define projection onto V along W. Now my question is

• we can take projections of x=y plane in yz plane in 3D euclidean geometry, this case after x=y would be precisely yz plane.




• But as per our definition of projection mapping, R^3 should be writen as direct sum of x=y plane and xz plane, but here is not so.




• Are they means different projections? I mean in euclidean 3D geometry we can take projections of plane onto a plane, but here in the definition of linear algebra about projection we cant take like this in 3D.




• So are not they denotes same projection?

May be my concepts are not clear at all. Please help me to clear out. Thanks in advance.

linear-algebra euclidean-geometry projection

share|cite|improve this question

edited Mar 28 at 4:09

user639336

asked Mar 28 at 3:56

user639336user639336

124

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Dude, you should work on your English. The last two points are completely non-understandable (at least to me).
  $endgroup$
  – amsmath
  Mar 28 at 4:03
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @amsmath I hope you are now comfortable in my last two lines. Sorry for the inconvenience caused. If the answer is know to you please submit in answer section. Thanks.
  $endgroup$
  – user639336
  Mar 28 at 4:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You might want to take another look at the definition of ”direct sum.”
  $endgroup$
  – amd
  Mar 28 at 4:50
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @amd sir I cant understand what you want to mean.
  $endgroup$
  – user639336
  Mar 28 at 4:51
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  A three-dimensional space cannot be the direct sum of a pair of its two-dimensional subspaces.
  $endgroup$
  – amd
  Mar 28 at 4:52
  

  
  
  
  

 | 
show 2 more comments

0

$begingroup$

I was reading about projection mapping in linear algebra between finite dimensional vector spaces. There were given a condition that my space should be written as direct sum of two of its subspaces V and W to define projection onto V along W. Now my question is

• we can take projections of x=y plane in yz plane in 3D euclidean geometry, this case after x=y would be precisely yz plane.




• But as per our definition of projection mapping, R^3 should be writen as direct sum of x=y plane and xz plane, but here is not so.




• Are they means different projections? I mean in euclidean 3D geometry we can take projections of plane onto a plane, but here in the definition of linear algebra about projection we cant take like this in 3D.




• So are not they denotes same projection?

May be my concepts are not clear at all. Please help me to clear out. Thanks in advance.

linear-algebra euclidean-geometry projection

share|cite|improve this question

edited Mar 28 at 4:09

user639336

asked Mar 28 at 3:56

user639336user639336

124

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Dude, you should work on your English. The last two points are completely non-understandable (at least to me).
  $endgroup$
  – amsmath
  Mar 28 at 4:03
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @amsmath I hope you are now comfortable in my last two lines. Sorry for the inconvenience caused. If the answer is know to you please submit in answer section. Thanks.
  $endgroup$
  – user639336
  Mar 28 at 4:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You might want to take another look at the definition of ”direct sum.”
  $endgroup$
  – amd
  Mar 28 at 4:50
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @amd sir I cant understand what you want to mean.
  $endgroup$
  – user639336
  Mar 28 at 4:51
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  A three-dimensional space cannot be the direct sum of a pair of its two-dimensional subspaces.
  $endgroup$
  – amd
  Mar 28 at 4:52
  

  
  
  
  

 | 
show 2 more comments

$begingroup$

I was reading about projection mapping in linear algebra between finite dimensional vector spaces. There were given a condition that my space should be written as direct sum of two of its subspaces V and W to define projection onto V along W. Now my question is

• we can take projections of x=y plane in yz plane in 3D euclidean geometry, this case after x=y would be precisely yz plane.




• But as per our definition of projection mapping, R^3 should be writen as direct sum of x=y plane and xz plane, but here is not so.




• Are they means different projections? I mean in euclidean 3D geometry we can take projections of plane onto a plane, but here in the definition of linear algebra about projection we cant take like this in 3D.




• So are not they denotes same projection?

May be my concepts are not clear at all. Please help me to clear out. Thanks in advance.

linear-algebra euclidean-geometry projection

share|cite|improve this question

edited Mar 28 at 4:09

user639336

asked Mar 28 at 3:56

user639336user639336

124

$endgroup$

share|cite|improve this question

edited Mar 28 at 4:09

user639336

asked Mar 28 at 3:56

user639336user639336

124

share|cite|improve this question

edited Mar 28 at 4:09

user639336

asked Mar 28 at 3:56

user639336user639336

124

asked Mar 28 at 3:56

user639336user639336

124

asked Mar 28 at 3:56

user639336user639336

124