That’s an old time question that it’s still a mistery to me. It’s a lot of time that I am trying to find an answer, but no text is clear on the topic and I am basically self-taught. What’s the difference between row vectors and column vectors? I came to this question when I found that the gradient was defined in two different ways on two different books. This was a problem and I started to look around: the more I was searching, the more it became a mistery, cause lot of books state that the gradient is the row vector of the first partial derivatives of a given function. I fixed this problem in the end (the gradient is not the row vector, but the column vector), but still I don’t get what’s the difference between row and columns, beyond a practical one in terms of computation. Does exist a "deep" theoretical difference between those two types of vectors or it's a metter of distinction between places (row vectors) and displacements (column vectors)? Thanks in advance!