Parenthesis vs brackets for matrices - next I have read Parenthesis vs brackets for matrices
and I currently use brackets matrices (quaternions in 3D computing, in fact).
But I still have a doubt about the strict compatibility of notations between brackets and parenthesis, as explained in the previous topic.
I do think brackets are orientation dependent where parenthesis are not, which goes with comas usage… It's my question
$$
\begin{pmatrix} 1, 2, 3, 6 \end{pmatrix}
·
\begin{pmatrix}  0, 1, 0, 0 \end{pmatrix}
= 
\begin{pmatrix} -2, 1, 6, -3\end{pmatrix}
$$
but
$$
\begin{bmatrix}
1 \\ 
2 \\
3 \\
6
\end{bmatrix}
·
\begin{bmatrix}
0 \\ 
1 \\
0 \\
0
\end{bmatrix}
= 
\begin{bmatrix}
-2\\ 
1\\ 
6\\ 
-3
\end{bmatrix}
$$
What's the truth ?
 A: Sometimes it is a matter of agreement. Many analysts use $(x_1,\ldots,x_n)$ to denote vectors of $\mathbb{R}^n$, while geometers and algebraists recommend
$$
\begin{pmatrix}
x_1 \\
\vdots \\
x_n
\end{pmatrix}.
$$
Indeed analysts often confuse, in $\mathbb{R}^n$, vectors and co-vectors (i.e. linear forms acting on vectors).
A: When you are working with only vectors in $\Bbb R^n$, then it is convenient (from the type-setting point of view) to put the coordinates in a row and separate them by commas as a simple list of data like
$$
(1+\epsilon,-1,x+y+z).
$$
Here parentheses are the most common (I guess because they are the most common delimiters), but it would be also acceptable to write
$$
[1+\epsilon,-1,x+y+z],
$$
everybody would understand.
However, if you are working with vectors in matrix context then it becomes important to distinguish between rows and columns (I guess that's what you mean by orientation). Here there are no commas used, and the column notation for vectors is preferable (because then one can write "matrix times vector" as $Ax$). It is often used the same parenthesis delimiters like
$$
\left(\begin{matrix}1+\epsilon & 1 & \frac{\pi}{2}\\-1 & 43 & 87\\ 1 & 1 & 1\end{matrix}\right)\left(\begin{matrix}1+\epsilon\\-1\\x+y+z\end{matrix}\right)
$$
but if the vector/matrix becomes taller some people think that it is too much empty space between. One may flatten them out as LaTeX does, for example, but then the parentheses look pretty much similar to brackets, and, in this case, the brackets may look aesthetically preferable (especially with hand-writing on the blackboard).
$$
\left(\begin{matrix}1+\epsilon\\-1\\12\\21\\32\\43\\54\\65\\x+y+z\end{matrix}\right),\quad \left[\begin{matrix}1+\epsilon\\-1\\12\\21\\32\\43\\54\\65\\x+y+z\end{matrix}\right]
$$
I do not think it is more than that in using different delimiters.
