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Is such a matrix possible?

  1. Mar 3, 2013 #1
    I want a matrix W of size nxk (where n>>k) with the following two properties:

    1. Sum of all elements of each row is equal to one, i.e. [itex]\sum[/itex]j wij = 1 for all i.
    2. Sum of squares of all elements of each column is equal to one, i.e. [itex]\sum[/itex]i wij2 = 1 for all j.

    Is such a matrix possible? Any hint at how to prove one way or the other would be appreciated. Thanks in advance.
     
  2. jcsd
  3. Mar 3, 2013 #2

    AlephZero

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    The simplest counter example is when k = 1 and n > 1.
     
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