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When I started studying math in 1982 in Germany, there seemed to have been a change in the choice of the default orientation of vectors; while it was row-vectors till then, it changed to column-vectors from then on.

My questions are, whether there actually was such a major change and, what were the reasons >and who the influential people and/or what the seminal publications were.

When was a default orientation for vectors defined for the first time and, was it widely accepted or have there been discussion about the proper choice?

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  • $\begingroup$ What makes you think there is a "default orientation" for vectors? Some people like matrices to act on the left, others on the right. In any case, this is not at the right level for MO and I've voted to close. $\endgroup$
    – Andy Putman
    Commented Jul 29, 2014 at 16:50
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    $\begingroup$ I think an overwhelming majority writes matrices on the left (and vectors as columns). Like almost all people write the function on the left of the argument: $f(x)$ or $fx$, not $(x)f$ :-) $\endgroup$
    – Alexandre Eremenko
    Commented Jul 29, 2014 at 17:15
  • $\begingroup$ @AlexandreEremenko the reason, why I asked is related to your argument: I suspect, that there has been a shift in the 'focus' of linear algebra: row vectors are the more natural choice, if one is interested in determining matrices (i.e. transformations that meet certain conditions); column vectors are the more natural choice, if the vectors are the unknown quantities like in least-squares problems. Would be interesting to learn, whether there actually was such a change and, where it came from. $\endgroup$
    – Manfred Weis
    Commented Aug 3, 2014 at 14:37
  • $\begingroup$ @AndyPutman I don't think that there is a default orientation for vectors; its similar to big-endian and little-endian in binary encoding of information: it is not so interesting that there are two options and that different people have different preferences, but it is (at least for me) interesting to learn the reasons why people change their mind and use the other option. $\endgroup$
    – Manfred Weis
    Commented Aug 3, 2014 at 14:49

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