Results 1 to 4 of 4

Math Help - Find if a linear transformation is flattening

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    11

    Find if a linear transformation is flattening

    I don't know if there's another term for the type of linear transform that collapses all points onto a line or the origin, but my book calls it a "flattening", and I'm wondering how you can tell if a transform is of a flattening type?
    The book I have says if one column of the matrix for the transform is a "scalar multiple" of the other, then it's flattening. Not quite sure what that means, however the example uses the matrix:

    2 3
    4 6

    And says the columns have a difference of 2/3 which means it's flattening, which confuses me as I thought scalar meant a whole integer? Any help/hints in this would be massively appreciated!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by NitrousUK View Post
    I don't know if there's another term for the type of linear transform that collapses all points onto a line or the origin, but my book calls it a "flattening", and I'm wondering how you can tell if a transform is of a flattening type?
    The book I have says if one column of the matrix for the transform is a "scalar multiple" of the other, then it's flattening. Not quite sure what that means, however the example uses the matrix:

    2 3
    4 6

    And says the columns have a difference of 2/3 which means it's flattening, which confuses me as I thought scalar meant a whole integer? Any help/hints in this would be massively appreciated!!
    A scalar is just a number (as opposed to, say, a vector or a matrix). It doesn't have to be a whole number. So 2/3, \sqrt2 and \pi are all scalars.

    The term "flattening" is not standard, but if the book chooses to uses, that's fine. (A mathematician would probably use the term singular matrix.) For a 22 matrix, there are various equivalent ways of defining this property. If you have met determinants, the simplest definition is probably to say that a matrix is flattening if its determinant is 0. Otherwise, you can use the definition in the book, that one column should be a scalar multiple of the other. In the case of the matrix \begin{bmatrix}2&3\\4&6\end{bmatrix}, each element in the left column is 2/3rds of the corresponding element in the right column. Another equivalent definition is that one row should be a scalar multiple of the other. In the case of that matrix, the bottom row is twice the top row.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    11
    Ah! Thanks!
    It really doesn't help my course chooses to use a lot of non-standard terminology, and not explain particularly well (Open University). I see now it means each element in one column being the same multiple of the corresponding element in the other column.
    Thanks for clearing that up!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,444
    Thanks
    1863
    The determinant of the matrix \begin{bmatrix}a & b \\ c & d\end{bmatrix} is ad- bc. If that equal 0, then ad- bc= 0 which is the same as ad= bc and, if b and d are not 0, \frac{a}{b}= \frac{c}{d} which says that one column is a multiple of the other.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 30th 2011, 04:36 PM
  2. Find the eigenvalues of the linear transformation:
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 26th 2010, 07:19 PM
  3. Find the basis of a linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 13th 2009, 02:02 PM
  4. Replies: 1
    Last Post: February 24th 2009, 02:19 AM
  5. Find a linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 1st 2008, 11:34 AM

Search Tags


/mathhelpforum @mathhelpforum