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My program generates orthogonal null space vectors such as this:

{{0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0}, {0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0}, {0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0}, {1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1}, {0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0}}.

My goal is to find the ordering which looks at the first occurrence of 1 within the vector. The desired ordering for the above is {5,1,2,6,3,4} corresponding to

{{1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0}}

Primitive attempts using Ordering and Sort have failed; my hope is someone can save me from the faux pas of a Do loop.

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  • 1
    $\begingroup$ Perhaps Reverse[Ordering[vecs]] ? $\endgroup$ – ilian May 18 '15 at 15:45
  • $\begingroup$ Yes, that's it as Martimer has shown. Thanks to you both. $\endgroup$ – dantopa May 18 '15 at 16:26
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Ordering[{{0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0},
{0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0},
{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0},
{1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1},
{0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0}}]//Reverse

{5, 1, 2, 6, 3, 4}

{{0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0},
{0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0},
{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0},
{1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1},
{0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0}}[[{5,1,2,6,3,4}]]

{{1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1},
{0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0},
{0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0},
{0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0},
{0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0},
{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0}}
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