Proper vector notation

notationvectors

I wrote a vector as $(a, b)$ in a maths exam but I was told it is not vector notation. However, I have seen this notation used all over this site and elsewhere. Is it correct or not?

Best Answer

This is a cultural thing. I think it's perfectly fine, in general. However, to give you some examples of why someone could find it non-fine:

  1. In secondary school (high school) here in Norway, students learn that the coordinates of points are written $(a, b)$, and the coordinates of vectors are written $[a, b]$. As my calculus book says, this leads to pedantic double bookkeeping, as there is no mathematical reason to distinguish between points in the plane and vectors in the plane.

  2. In linear algebra, the coordinates of your everyday vectors are usually written in column form: $\left(\begin{smallmatrix}a\\b\end{smallmatrix}\right)$, or $\left[\begin{smallmatrix}a\\b\end{smallmatrix}\right]$. Writing it as $(a, b)$ makes it a row vector, which is a different kind of object.

  3. As pointed out in the comments: Some don't like using coordinates at all, and want you to explicitly write your vectors as linear combinations of the unit vectors, giving something along the lines of $a\vec i + b\vec j$ or $a\vec{e_x} + b\vec{e_y}$.

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