Orthogonal Projection with a unit vector [on hold]

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I have a line in R^2 that contains the unit vector u = [u1;u2]. How can I find the orthogonal projection onto L?



How can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T




linear-algebra orthogonality projection-matrices




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put on hold as off-topic by Hans Lundmark, Taroccoesbrocco, José Carlos Santos, Henrik, Claude Leibovici 2 days 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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Hans Lundmark, Taroccoesbrocco, José Carlos Santos, Henrik, Claude Leibovici
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Consider the projection matrix and see what it does @KhanMan
    – Anik Bhowmick
    2 days ago






  • 1




    What are your thoughts about that? What have you tried so far?
    – Taroccoesbrocco
    2 days ago










  • Try to formularize your question, your words don't seem enough clear, what you really want exactly.
    – peterh
    2 days ago










  • @peterh how can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T
    – KhanMan
    2 days ago










  • @KhanMan Edit it into the question.
    – peterh
    2 days ago














up vote
-3
down vote

favorite












I have a line in R^2 that contains the unit vector u = [u1;u2]. How can I find the orthogonal projection onto L?



How can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T




linear-algebra orthogonality projection-matrices




share|cite|improve this question













put on hold as off-topic by Hans Lundmark, Taroccoesbrocco, José Carlos Santos, Henrik, Claude Leibovici 2 days 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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Hans Lundmark, Taroccoesbrocco, José Carlos Santos, Henrik, Claude Leibovici
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Consider the projection matrix and see what it does @KhanMan
    – Anik Bhowmick
    2 days ago






  • 1




    What are your thoughts about that? What have you tried so far?
    – Taroccoesbrocco
    2 days ago










  • Try to formularize your question, your words don't seem enough clear, what you really want exactly.
    – peterh
    2 days ago










  • @peterh how can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T
    – KhanMan
    2 days ago










  • @KhanMan Edit it into the question.
    – peterh
    2 days ago












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











I have a line in R^2 that contains the unit vector u = [u1;u2]. How can I find the orthogonal projection onto L?



How can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T




linear-algebra orthogonality projection-matrices




share|cite|improve this question













I have a line in R^2 that contains the unit vector u = [u1;u2]. How can I find the orthogonal projection onto L?



How can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T





linear-algebra orthogonality projection-matrices





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 2 days ago
























asked 2 days ago









KhanMan

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put on hold as off-topic by Hans Lundmark, Taroccoesbrocco, José Carlos Santos, Henrik, Claude Leibovici 2 days 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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Hans Lundmark, Taroccoesbrocco, José Carlos Santos, Henrik, Claude Leibovici
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 Hans Lundmark, Taroccoesbrocco, José Carlos Santos, Henrik, Claude Leibovici 2 days 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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Hans Lundmark, Taroccoesbrocco, José Carlos Santos, Henrik, Claude Leibovici
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Consider the projection matrix and see what it does @KhanMan
    – Anik Bhowmick
    2 days ago






  • 1




    What are your thoughts about that? What have you tried so far?
    – Taroccoesbrocco
    2 days ago










  • Try to formularize your question, your words don't seem enough clear, what you really want exactly.
    – peterh
    2 days ago










  • @peterh how can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T
    – KhanMan
    2 days ago










  • @KhanMan Edit it into the question.
    – peterh
    2 days ago
















  • Consider the projection matrix and see what it does @KhanMan
    – Anik Bhowmick
    2 days ago






  • 1




    What are your thoughts about that? What have you tried so far?
    – Taroccoesbrocco
    2 days ago










  • Try to formularize your question, your words don't seem enough clear, what you really want exactly.
    – peterh
    2 days ago










  • @peterh how can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T
    – KhanMan
    2 days ago










  • @KhanMan Edit it into the question.
    – peterh
    2 days ago















Consider the projection matrix and see what it does @KhanMan
– Anik Bhowmick
2 days ago




Consider the projection matrix and see what it does @KhanMan
– Anik Bhowmick
2 days ago




1




1




What are your thoughts about that? What have you tried so far?
– Taroccoesbrocco
2 days ago




What are your thoughts about that? What have you tried so far?
– Taroccoesbrocco
2 days ago












Try to formularize your question, your words don't seem enough clear, what you really want exactly.
– peterh
2 days ago




Try to formularize your question, your words don't seem enough clear, what you really want exactly.
– peterh
2 days ago












@peterh how can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T
– KhanMan
2 days ago




@peterh how can I find the orthogonal projection onto L. If I already have unit vectors, then I do not need to go through grand-schmidt? So I can use these unit vectors as my orthonormal basis, and just directly plug into A(A^T*A) ^−1*A^T
– KhanMan
2 days ago












@KhanMan Edit it into the question.
– peterh
2 days ago




@KhanMan Edit it into the question.
– peterh
2 days ago















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