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Set of vectors with each subset forming a basis

  1. Nov 24, 2012 #1
    Hey!

    Let M and N be two natural numbers and N>M. I want to build a set A with N vectors of size M such that each subset S of A, where |S| = M, contains linearly independent vectors.

    Another way to put it is that every S should be a basis for R^M.

    Any ideas? Thanks!
     
  2. jcsd
  3. Nov 26, 2012 #2
    Do you want an explicit construction or a proof that such a set exists?
     
  4. Nov 27, 2012 #3

    HallsofIvy

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    For example, if M= 2, you can take i= <1, 0>, j= <0, 1>, and k= i+ j= <1, 1>. Then any subset of order 2, {i, j}, {i, k}, and {j, k}, is a basis.

    For M= 3, start with i= <1, 0, 0>, j=<0, 1, 0>, and k= <0, 0, 1> and add l= i+ j+ k.

    Can you continue that?
     
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