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Homework Help: Transformation matrix question

  1. Aug 1, 2006 #1
    Show by direct expansion that [tex]| \lambda | ^2 =1 [/tex]

    For simplicity, take [tex]\lambda[/tex] to be a two-dimensional transformation matrix.

    from what I understand, if X was a vector (2,3,4), [tex]| X | [/tex] is finding the length of the vector by adding the square of the numbers and taking a square root. [tex]\sqrt{2^2+3^2+4^2}[/tex]

    What I dont understand is how to apply this to a matrix

    because a 2x2 matrix times itself is still a 2x2 matrix, and even after one square root's it, it's still a 2x2 matrix, never just 1.

    What am I missing?
     
  2. jcsd
  3. Aug 1, 2006 #2

    HallsofIvy

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    You are missing just about everything! What do you mean "For simplicity, take [itex]\lambda[/itex] to be a two-dimensional transformation matrix"? Is that given as part of the problem? Why "for simplicity"? If you are not told what [itex]\lambda[/itex] is, the problem makes no sense at all.

    Exactly what is a "transformation matrix"? You can't mean what I would think it means because it simply is not true that the determinant of every transformation matrix is 1. And it would be a really good idea to look up "determinant of a matrix". If you were asked to do this problem, then you were certainly expected to know what that is and how to calculate it!
     
  4. Aug 1, 2006 #3
    The question just asks

    "Show by direct expansion that [tex]| \lambda | ^2 =1 [/tex] For simplicity, take [tex]\lambda[/tex] to be a two-dimensional transformation matrix."

    your guess is as good as mine as to what is a transformation matrix.
    And it's not "the determinant of every transformation matrix is 1" it's the determinant squared is equal to one, which also doesnt make sence because I thought that [tex]1=| \lambda | |\lambda|^{-1}[/tex]
     
  5. Aug 2, 2006 #4
    is this a possible description:

    [tex] 1= | \lambda | ^2 =| \lambda | |\lambda|^{-1} [/tex]

    I'm not really sure on this...
     
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