How should I write a vector? as a row or column matrix?
I ask this question because I see many people including me that writing a vector both ways in linear algebra, but now that I think about it it should not be that way, did ever someone defined it?
Thank you in advance.
Best Answer
It's rather arbitrary but it makes sense to restrict yourself to one or the other to avoid confusion. The column vector convention has notational similarities with $f(x)$ notation, which gives the function on the left in the same way we might multiply a column vector on the left by a matrix in the form $Ax$. There is no reason you cannot do all of this backwards though by establishing the row vector and multiplying on the right as $xA$. I would also point out that rows and column vectors are not the only choices you have. For example the space of two by two matrices with coefficients in a field form a vector space over that field as well and is neither a column or row vector. If one form or another is prefered it often has more to do with the linear transformations you intend to apply to the vector and how you want to organize the notation for readability.