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Linear algebra-how do I know if something is invertible?

  1. Feb 23, 2008 #1
    Linear algebra--how do I know if something is invertible?

    Say I have a "reflection about the line y = x/3 in R^2," how do I know if the function or "T" is invertible?

    Thank you.
  2. jcsd
  3. Feb 23, 2008 #2
    T is inv if its matrix is invertible, I think reflecting about y = x/3 function/T is invertible .

    just use vertical/horizontal line test for functions
  4. Feb 23, 2008 #3
    Well you could first find out what the matrix representation of this linear transformation is. Are you familiar with these terms?
  5. Feb 23, 2008 #4
    yes, but how does the vertical line test work?
  6. Feb 23, 2008 #5
    I don't think it would work on transformations >>

    for functions draw a vertical line, if it passes through the function twice then that means your function is not an actual function

    and for inverse, draw horizontal line ...

    something really simple stupid that I never used
  7. Feb 24, 2008 #6
    Well there is an invertible transformation for any reflection across a line through the origin.
  8. Feb 24, 2008 #7


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    Staff Emeritus
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    Geometrically, if you reflect a second time across the same line, you are right back where you started. Any reflection is its own inverse.
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