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Quick Question: Is this matrix an orthogonal projection?

  1. Apr 23, 2008 #1
    [SOLVED] Quick Question: Is this matrix an orthogonal projection?

    1. The problem statement, all variables and given/known data
    P=[0 0 ]
    [11]


    2. Relevant equations



    3. The attempt at a solution

    Its orthogonal if the null space and range are perpendicular.
    Range=[0 ]
    [x+y]
    null space=[x
     
  2. jcsd
  3. Apr 23, 2008 #2
    null space=[x ]
    [-x]??
    So then its not orthogonal??
     
  4. Apr 24, 2008 #3

    Dick

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    Science Advisor
    Homework Helper

    If you mean the range is spanned by the vector [0,1] and the null space is spanned by the vector [1,-1] (which I think you do mean) then yes, not orthogonal.
     
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